Ex 95, 6 Show that the given differential equation is homogeneous and solve each of them 𝑥 𝑑𝑦−𝑦 𝑑𝑥=√(𝑥^2𝑦^2 ) 𝑑𝑥 Step 1 Find 𝑑𝑦/𝑑𝑥 x dy − y dx = √(𝑥^2𝑦^2 ) dx x dy = √(𝑥^2𝑦^2 ) dx y dx x dy = (√(𝑥^2𝑦^2 )𝑦) dx 𝑑𝑦/𝑑𝑥 = (√(𝑥^2 𝑦^2 ) 𝑦)/𝑥 Step 2 Put 𝑑𝑦/𝑑𝑥 =A curve through (1, 0) and satisfying the differential equation (1 y2)dx xy dy = 0 is (A) a circle (B) a parabola an ellipse (D) a hyperbola 详细过程请见下图,希望对亲有帮助 (看不到图的话请Hi我) 希望对亲有帮助 围成D的三条直线分别是 AB：y = x/2 1/2 BC：y = 3x
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6. (x^(2)-y^(2))dx-xydy=0- (x²xyy²)dxxydy=0 answer with solution asistinsilverlp8ut9y is waiting for your help Add your answer and earn pointsD/dx x^2 y^4, d/dy x^2 y^4 WolframAlpha Have a question about using WolframAlpha?
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(y^22xy)dx (x^2) dy = 0 Integrating factor y^2 solution xx^2/y = C Finding the integrating factor Giving these things some names names M(x,y) = y^22xy N(x,y) = x^2 M(x,y) dx N(x,y) = 0 We're looking to make this an exact equation, because if we do, it can be solved rather systematically In order to be exact, by claurait's theoem (think that's the name ofAvail 25% off on study pack Avail OfferApply suitable substitution, solve these equations by separation variable method (i) (x 22 y 2) dx xydy = 0 (ii) x 2 y 03 xy2 y 2 = 0 (iii) y 2 x 2 dy dx = xy dy dx (iv) (x y) dy = (yx) dx (v) x sin(y x) dy dx = y sin(y x) x (vi) x 3 dy dx = y 3 y 2 p y 2x 2 (vii) 2 y exp(x/y) dx (y2 x exp(x/y)) dy = 0 (viii) (x exp(y/x)y
Learn how to solve differential equations problems step by step online Solve the differential equation xy*dx(1x^2)dy=0 Grouping the terms of the differential equation Group the terms of the differential equation Move the terms of the y variable to the left side, and the terms of the x variable to the right side Simplify the expression \frac{1}{y}dy Integrate both sides of theSolution for 2 (2x^2y^2)dx (xy)dy=0 equation Simplifying 2 (2x 2 y 2) * dx 1 (xy) * dy = 0 Reorder the terms for easier multiplication 2dx (2x 2 y 2) 1 (xy) * dy = 0 (2x 2 * 2dx y 2 * 2dx) 1 (xy) * dy = 0 Reorder the terms (2dxy 2 4dx 3) 1 (xy) * dy = 0 (2dxy 2 4dx 3) 1 (xy) * dy = 0 Multiply xy * dy 2dxy 2 4dx 3 1dxy 2 = 0 Reorder the terms 2dxy 2 1dxy 2The line y = mx 1 is a tangent to the curve y2 = 4x Find the
Solve (x^2y^2x)dxxy dy =0 Get the answers you need, now! Ex 95, 4 show that the given differential equation is homogeneous and solve each of them (𝑥^2−𝑦^2 )𝑑𝑥2𝑥𝑦 𝑑𝑦=0 Step 1 Find 𝑑𝑦/𝑑𝑥 (𝑥^2−𝑦^2 )𝑑𝑥2𝑥𝑦 𝑑𝑦=0 2xy dy = − (𝑥^2−𝑦^2 ) dx 2xy dy = (𝑦^2−𝑥^2 ) dx 𝑑𝑦/𝑑𝑥 = (𝑦^2 − 𝑥^2)/2𝑥𝑦 Step 2 Putting F(x, y) = 𝑑𝑦/𝑑𝑥 and finding F (xsqrt (x ^ (2) y ^ (2)) y ^ (2)) dx xydy = 0 সমাধান Updated On 72 To keep watching this video solution for FREE, Download our App Join the 2 Crores Student community now!
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The general solution of the differential equation √(1 x^2 y^2 x^2y^2) xy(dy/dx) = 0 is (where C is a constant of integration)For the equation (x^2 y^2 x)dx xydy =0 , take xy=V(x) Obtain ( x^2 V^2/x^2 x )dx V( xdV Vdx)/x^2 =0 Then (x^2 x)dx VdV/x =0Separating (x^3 x^2)dx = VdV Integrating obtain the solution 6x^2y^2 4x^3 3x^4 = C I Solve the following problem (please show the whole procedure) Show transcribed image text Expert Answer Who are the experts?
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Solve x(√(x²y²)) y²dx xydy=0 Share with your friends Share 1 x x 2 y 2y 2 dx xy dy = 0 x x 2 y 2y 2 dx =xy dy dyNext Previous Related Questions Solve the following equations calculate y^''' for y=e^x/x If , then for what value of a is A an identity matrix? solve y^3 dx2 (x^3xy^2) dy=0 asked in PRECALCULUS by anonymous differentiation if y = (3x^3) (e^ (2x))/ Inx Find d^2y/dx^2 asked in CALCULUS by linda Scholar derivatives usingchainrule
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Watch Video in App This browser does not support the video element 412 k 358 k Answer Given, √(1x 2 y 2 x 2 y 2) xydy/dx=0 By simplifying the equation, we get Now substituting these value of t and m, we get Question 21 x√(x 2 y 2) – y 2dx xydy = 0 Solution We have, x√(x 2 y 2) – y 2dx xydy = 0 dy/dx = x√(x 2 y 2) – y 2/xy dy/dx = y 2 – x√(x 2 y 2)/xy It is a homogeneous equation, So, put y = vx (i) On differentiating both sides wrt x, dy/dx = v x(dv/dx) So, v x(dv/dx) = v 2 x 2 – x√(x 2 v 2 x
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The GS is y^2 = (A x^4)/(2x^2) Or, alternatively y = sqrt(A x^4)/(sqrt(2)x) We have (x^2 y^2) \ dx xy \ dy = 0 Which we can write in standard form as dy/dx = (x^2 y^2)/(xy) 1 Which is a nonseparable First Order Ordinary Differential Equation`therefore x^2 y^2 = cx`, where c is constant which is the required general solution Concept Methods of Solving First Order, First Degree Differential EquationsDescribe the Transformation y=3(x2)^21 The parent function is the simplest form of the type of function given Simplify Tap for more steps Simplify each term Tap for more steps Rewrite as Expand using the FOIL Method Tap for more steps Apply the distributive property
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X 3 y x 2 y 2 12 0 2x y 1 y 2 = (x2 y2 1)dx xydy =0 25 (x2 −1)y′sin y 2xcos y =2x −2x3 Đặt z =cos y 26 x(eyClick here👆to get an answer to your question ️ Solve (x^2 y^2)dx xydy = 0 Join / Login > 12th > Maths > Differential Equations > Solving Homogeneous Differential Equation The solution of the DE y y 1 = x x 2 y 2 how to solve 3xy y 2 dx x 2 xy dy 0 also i wish to knw when to use y vx or x vy Mathematics TopperLearningcom h9faf2xx Starting early can help you score better!
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We can rewrite this Ordinary Differential Equation in differential form (x2 y2) dx − xy dy = 0 A as follows dy dx = x2 y2 xy ∴ dy dx = x y y x B Leading to a suggestion of a substitution of the form u = y x ⇔ y = uxContact Pro Premium Expert Support »Solve ( x 2 y − 2 x y 2) d x − ( x 3 − 3 x 2 y) d y = 0 written 34 years ago by smitapn612 ♦ 90 modified 15 months ago by sanketshingote ♦ 570 ADD COMMENT 1 Answer 1 658 views written 34 years ago by smitapn612 ♦ 90 modified 33 years ago by awariswati1 ♦ 770
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` (x^(2)y^(2)) dx 2xy dy = 0`For the homogeneous equation (x^2 xy y^2)dx xydy =0, take y =xV(x) The equation becomes (1 V)dx xVdV =0 Separating dx/x = VdV/(V1) = dV dV/(V1) Integrating gives lnx = V ln(V1) lnC Then ln((V1)x/C)= V Follows the solution y = x Ce^(y/x) x 2 d x − y 2 d x x d y 2 = 0 d x x d y 2 − y 2 d x x 2 = 0 d x d ( y 2 x) = 0 x y 2 x = C It seems to me that there is a sign mistake somewhere Share edited Nov 11 ' at 2301 answered Nov 11 ' at 2256 Aryadeva
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Q2 The general solution of the differential equation (y2 – x3)dx – xydy = 0 (x 0) is (where c is a constant of integration) (1) y 2 2x 2 cx 3 = 0 (2) y 2 2x 3 cx 2 = 0Solve the homgenous equation (x^2 xy y^2) dx xy dy = 0 using an appropriate substitution (y=ux, dy=udx xdu) or (x=vy, dx=vdy ydv) Please show all steps and verify the answer yx = cx 2 e (y/x)An alternative approach showing how to arrive at the right integrating factor Split the terms in two groups as follows $$2x^2dx(y^2dxxydy)=0$$ Now for $2x^2dx$ the integrating factor is trivial $1$ leading to solution $x^3=C$ Then $\mu_1=\phi(x^3)$ where $\phi$ is an arbitrary function will be the most general integrating factor for this part
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The general solution of the differential solution of (y 2 – x 3 )dx – xydy = 0 (x ≠ 0) is (Where c is the integration constant) A y2 – 2x2 cx3 = 0Experts are tested by Chegg as specialists in their subject area We review their content and use your feedback to keep the quality high Transcribed image text (x2 3y2)dx – 2xydy = 0 y (2) = 6To elaborate, divide by x y to get y ′ = y 2 x x y Put u = y / x, y ′ = x u ′ u x u ′ u = u 2 u General solution of (x^2y^2)dx (3xy)dy = 0 General solution of ( x 2 − y 2 ) d x ( 3 x y ) d y = 0
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The given differential equation ie, (x 2 xy) dy = (x 2 y 2) dx can be written asThis shows that equation (1) is a homogeneous equation To solve it, we make the substitution as y = vx Differentiating both sides with respect to x, we get(a) (y 2 − √ x 2 y 2) dx−x 2 dy= 0 (b) (x 2y−1)dx= (x 2y−3)dy (c) (y− √ x 2 y 2) dx−xdy= 0 (d) tan (y x) dy− x 2 y 2 x dx xydy = 0 Sol solutionpdf Do you need an answer to a question different from the above?
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X 2 1) dx−xydy= 0 (b) xdy (3x− 2 y)dx= 0 (c) 2xdy (2 x 2) dy= 0 (d)x 2 ydy−ydx= 0 Which of the following is a differential equation with homogeneous coefficient?Soul soul Math Secondary School answered Solve (x^2y^2x)dxxy dy =0 2 See answers sjasmit sjasmit Stepbystep explanation U FIRST FOLLOW ME PLZ MATE PLZ FOLLOW ME Brainly User Brainly UserCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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113k views asked in Class XII Maths by nikita74 (1,017 points) Find the general solution of y 2 dx (x 2 xyy 2 )dy = 0 differential equations For the differential equation `(x^2y^2)dx2xy dy=0`, which of the following are true (A) solution is `x^2y^2=cx` (B) `x^2y^2=cx` `x^2y^2=xc` (D) `yP(x,y)dxQ(x,y)dy = 0 where P(x,y) = 2(y 1)ex Q(x,y) = 2(ex −2y) ∂P ∂y = 2e x = ∂Q ∂x, ∴ ode is exact ∴ u(x,y) exists such that du = ∂u ∂x dx ∂u ∂y dy = P dxQdy = 0, Giving i) ∂u ∂x = 2(y 1)e x, ii) ∂u ∂y = 2(e −2y) Integrate i) u = 2(y 1)ex φ(y) Differentiate ∂u ∂y = 2e x dφ dy = 2(e x
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X y ⋅ d y d x = 4 x 2 2 y 2 xy \cdot \dfrac {dy} {dx} = 4x^22y^2 x y ⋅ d x d y = 4 x 2 2 y 2 Divide the equation by x 2 x^2 x 2 y x ⋅ d y d x = 4 2 y 2 x 2 (1) \dfrac {y} {x} \cdot \dfrac {dy} {dx} = 4 2 \dfrac {y^2} {x^2} \tag {1} x y ⋅ d x d y = 4 2 x 2 y(x 2 y 2) d x − 2 x y d y = 0 is the given equation Before we start solving it, we must know what type of differential equation it is The given equation can be rewritten as d y d x = x 2 y 2 2 x y Now x 2 y 2 2 x y is a homogeneous function of degree zero So it is a homogeneous differential equation and hence we will use the methodTheory Roots of a product 51 A product of several terms equals zero When a product of two or more terms equals zero, then at least one of the terms must be zero We shall now solve each term = 0 separately In other words, we are going to solve as many equations as there are terms in the product Any solution of term = 0 solves product
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To elaborate, divide by x y to get y ′ = y 2 x x y Put u = y / x, y ′ = x u ′ u x u ′ u = u 2 u General solution of (x^2y^2)dx (3xy)dy = 0 General solution of ( x 2 − y 2 ) d x ( 3 x y ) d y = 0Solution for (x^2y^2)dx (x^2xy)dy=0 equation Simplifying (x 2 y 2) * dx (x 2 1xy) * dy = 0 Reorder the terms for easier multiplication dx (x 2 y 2) (x 2 1xy) * dy = 0 (x 2 * dx y 2 * dx) (x 2 1xy) * dy = 0 Reorder the terms (dxy 2 dx 3) (x 2 1xy) * dy = 0 (dxy 2 dx 3) (x 2 1xy) * dy = 0 Reorder the terms dxy 2 dx 3 (1xy x 2) * dy = 0 Reorder the terms for easier multiplication dxy 2 dx 3 dy (1xy x 2) = 0 dxy 2 dx 3 (1xy * dyGiven The homogeneous differential equation is given as, (x2y2)dxxydy =0 ( x 2 y 2) d x x y d y = 0 To find the solution
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