Find the solution of the initial value problem: y (4) -6y +9y"=0 [y(0) = -2, y' (0) = -3, y" (0) = 0, y" (0)=0] a) b) c) d) e) y=-3-2x y=-2-3x 3 y=-3 e³x-2x e³x y = −2+3x 3 y=-2 e³x -3xe³x f) None of the above.

Q: 5) Find the general solution of the following equation y" +8 y"-9 y=0

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Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: 2x y" +5xy' + y = 3x +2 Answer y(x) = +은+2+

A: The given equation is of the form ax2y''+bxy'+cy=g(x) The solution to the above equation is given by…

Q: 8.) y" +2y' +5y = 3e 2* ; and y(0) = y'(0) = 1

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Q: (e) y(ª) – 4y "= 5x² -e2* (g) y(“) +8y '= 4

A: The given differential equation is y(4)-4y''=5x2-e2x

Q: Obtain general solution. 1) y''-y=ex-4

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Q: 9. y" +9y = 0

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Q: (C) y" + 21y+8x=y" + 5y' + e²*

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Q: 5. Solve, using the method of undetermined coefficients: y" + 2y' = 2x + 5 – e-2= %3D

A: First we shall get particular solution of y''+2y'=2x+5. Using method of undetermined coefficients y…

Q: (h) xy" + 8y' +18xy = 0, xo = 1 (i) (3 — x²)y" — 8xy' - 18y = 0, xo = 0 (j) 2y" + 8xy' + 18y = 0, xo…

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Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

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Q: Find the general solution of x2y" - (2a-1)xy' + a²y = xa+1 where a is a constant.

A: Given  x2y'' - 2a - 1xy + a2y = xa+1  ----------(1)           This is Cauchy's homogeneous…

Q: 1) Find the general solution of the equation x³y"" - 2x2y" - 4xy' + 8y = x² + lnx.

A: In this question we will find the general solution of the differential equations.

Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

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Q: (3) y "'- 2y "– 4y '+8y = 6xe²* %3D

A: Note: " As per our guidelines we will solve only first question . If you want any specific question…

Q: Solve y(H) a) Y (6) = y (4) = ? %3D b) y"-y' • 24 ylo)=1;y'(0)=-2 %3D

A: We have to find the solution y(t) from the following  a) y(s)=1s2(s2+1) b) y''-y'=2t, y(0)=1,…

Q: 8. Solve the Cauchy-Euler equation 4x²y" + 8xy' + y = 0.

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Q: 1) Find the general solution of the equation x³y" - 2x²y" - 4xy' + 8y = x² + Inx.

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Q: Evaluate the general solution of y""=e4x + sinx

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Q: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: (3) y" – 25y = 2xe"

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Q: (1) y "'+ y "– 2y = 3+2cosx

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Q: y" + 7y' + 10y = -1lte".

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: If r2+ 2r –1 = 0 is the characteristic equation of a homogeneous D.E. with constant coefficients,…

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Q: Find general solution y = Yc + Yp of y(3) + y" 3e" + 4x2

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Q: - Sapotri to solve 2x?y" – my + (x + 1)y = 0. n=0 12) Use y =

A: Given: 2x2y''-xy'+x+1y=0. To Do: Solve the given differential equation using y=∑n=0∞anxn+r.