Verify if the given equation is a solution of the given differential equation. Show full solution.

Q: (3y²-x²» = 0 ;when x = 1, y = 1 2y4

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Q: au au = xt at (x > 0,t > 0) ax u(0, t) = 0 u(x,0) = 0

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Q: 6. 7. 8. dy x- -= x² + y y = x² + 4x; dx In y = C₁e* + c₂e-x; yy" - (y')² = y² In y y−³ = x³ (3ex +…

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Q: (16x y² exy + y sec² (xy) - 2x + 3y) + (16x² y e4xy + x sec² (xy) + 3x)y' = 5

A: Let us consider the equation Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x The solution of the…

Q: (e"siny + tany)dx + (e*cosy + xsec*y)dy = 0

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Q: 2x dy 2х. -y = x² - x; y(4) =2 dx

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Q: (4x'у — 15х? — у )ӑx +x* +3у? - х)dy-0

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Q: x x + x = 0 x + x 3

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Q: 1. By applying the method of undetermined coefficients, find the general solution of the following…

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Q: c) (y')Va? - 16 = 11x d) yy -10e2t = 0

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Q: y (t) = cie' + czet – 3te + cos t –

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Q: y" + y = secx tan x

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Q: (x² + 2xy- 4y?)dx- (x² – 8xy– 4y²)dy=0 | O x² + 4y² = C(x + y) O x2 +y2 = C(x+ 4y) O x2 + 2y? = C(x…

A: Solution(x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0dydx=x2+2xy-4y2x2-8xy-4y2(∙)this differential equation is…

Q: du х — у— 1

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Q: dy xy' = 6y + 12x*ys, (y' = dx

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Q: d5u d*u d?u 7. — 18и 3D 0 dt2 dt5 dt4

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Q: 4. y" +y = 2xsinx

A: First we will find complimentary function and the perticular function.

Q: 1. (у — 2)dx — (х — у — 1)dy %3D 0 |

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Q: 4. t dv + (v – v² ln t)dt = 0

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