In the differential equation, (D3 – 2D2 – 3D)y = 0; assume a. y, = A + Be-* + Ce3* b. y, = A + Be* + Ce-3x C. y, = A + Be* + Ce-3x d. y. = A + Be* + Ce3x

Q: Eliminate the constant: 2x 3x =c₂₁e²x + c₁₂e³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

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Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: give me the solution of   y'' - 2y'- 2y = 0

A: Topic:- differential equation

Q: d) Solve: y"+y"-5y' + 3y = 0

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Q: y” – 10y’ + 25y = 30x+3

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Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: 8. y" – y = 5sin²(x); when y(0) = 2, y'(0) = -4 %D

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Q: Solve (D² – 3D + 2) y = 2e3 +4 sec (e-)

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Q: Write down two linearly independent solutions of the Bessel equation 16x?y" + 16ry + (162 – 9) y =…

A: The given differentiate equation can be written as:

Q: . Find the general solution of the first-order equation y? – 2ry dy dr

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Q: A -3 0 1 -3

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Q: Reduce the equation yzxx + (x + y)2xy + XZyy = 0 to a canonical form and solve it.

A: The characteristics integrals:

Q: -4x y"+6y'+9y=7+

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Q: The complementary function(C.F.) of the differential equation(D – 2)°y = sin 2x is_ O (ci + c2x +…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: Let 1 2 -1 A = 2 4 -2 -2 Describe all solutions of A = 0. * = x2 +x3 +x4

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Q: In(-/-) (vi) 2x In - x = 0

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Q: Solve ylk + 2) + 2yjk + 1} + v[k] = 0 if y[-1] = 1, y[–2] = 1 %3D

A: Given,                            y[k+2]+2y[k+1]+y[k]=0                               ...(1)…

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: how did this equation Hx = exp P (ny + ). ož = vi[exp (o,) – 1] turned into this equation 1 In Hy =…

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Q: 1. Describe and solve each first-order equation. 2 2 (a) x²y'=xy²+3y² (b) y'+3y=3t²e-30

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Q: Find the general solution of the fifth-order DEQ. 2x(5) – 7x(4) + 12x" + 8x" = 0

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Q: y₁=1+a3x³ + arº +... Y₂ = x + b₁x¹ + b₁x² + ... Enter the first few coefficients: a3 = a6 = b₁ b7 )…

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Q: d²x 7x + 3- dt2 dt 2- - t dx

A: 7x+3d2xdt2=2dtdx-t Multiplying both sides by dxdt , we get 7xdxdt+3d2xdt2dxdt=2-tdxdt              1

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: If y = x2 is one solution of x2y''+2xy'-6y=0 and the other linearly independent solution.

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Q: Solve the following linear system and sketch its phase portrait * = [¹ =1] x.

A: Here for a given homogeneous matrix linear system we have to solve it and then sketch the phase…

Q: y" + 2y'-3y 7x-3x.

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Q: Consider the non-linear differential equation * =- x+ y – 1 ў 3 2х + х3. Draw the nullclines and a…

A: Regression Analysis:              Regression analysis helps to estimate the changes when…

Q: 1.² T 20 40x-x² 9√x²+y2 dydx=

A: We have to solve ∫020∫x40-x29x2+y2dydxThe region bounded by0≤x≤20x≤y≤40x-x2⇒x=y and y=40x-x2squaring…

Q: Re(2²) = 1

A: To solve the equation: Re(z2)=1                                                      (1) Here z is a…

Q: j'+7y'+12y=2le", y(0); (0)=,"'(0)= -10. 10)=-10 .

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Q: The differential operator (D2 - 16D+113)³ annihilates the functions

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Q: 2xy y' + 2x² x' = y² x'

A: Given: 2xyy' + 2x3x' = y2x' ⇒2xydy + 2x3dx = y2dx ⇒2xydy- y2dx=- 2x3dx