- C3e³z y = C1 + C2e -4x = c1e² + c2e²¤ + c3e³z

Q: y''-4y'+8y=x3, y(0)=2, y'(0)=4

A: Given y’’ -4y’ +8y=x3 ------1 Y(0) =2, y’(0) =4 Auxilliary equation corresponding to homogeneous…

Q: i=r(1-rX4-r'), = 2–r?

A: The given system of differential equation in polar form is: r˙=r1-r24-r2θ˙=2-r2 Therefore the…

Q: y" - 8y + 25y = 0; y(0) = 0, y'(0) = 3

A: y''-8y'+25y=0; y(0)=0, y'(0)=3 We have to solve it using Laplace transform.

Q: (9y² + y - 7) + (7y² -y-4) = ]

A: We have to add 9y2+y-7+7y2-y-4

Q: y" + y' -2y = 3 -6t. y(0) = -1. y'(0) = 0

A:

Q: y"" - 4y" + 5y' - 2y = 7t-5, y(0) = 0, y'(0) = 0, y'(0) = -2

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Q: y''-7y +10=0, y(0)= 2 and y'(0) = 4

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Q: y = cez + c2xe None of the others y = cez + xe³z

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Q: * + y - 2 = 0 O C. r + y + 2z = 9

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Q: y"" + 2y" - 11y' - 12y = 11t-9, y(0) = 0, y' (0) = 0, y" (0) = -3

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Q: r: 2) y' - 2y = 2e5t + 5e²t, with y(0) = -3

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Q: y2 + 3y - 11 = (y + 2)(y - 4)

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Q: y" - y' - 12y = 0, y(0)=3, y'(0)=5

A: The given differential equation is y''-y'-12y=0 and the given initial conditions are y(0)=3 and…

Q: y"-3y-2y=0; x = 0, y = 0, y =9, y'=0

A: Solution of given question is written in below steps.

Q: y =2x+y?, y(0) = - 1

A:

Q: (i) y"-10y'+9y=5t, y(0)=-1, y'(0)=2

A: As you asked more than one question I solved the first one.

Q: y" – 6y + 10 y = 50 x + 3e - +20

A: We are asked to solve the differential equations.

Q: y" + 5y' + 6y = 12, y0 = 2, y'0 = 0

A: Consider the given differential equation y''+5y'+6y=12 ,   y0=2, y'0=0            …1 The homogeneous…

Q: 3y-6(y+z)+y

A: Distribute -6.

Q: y""-4y" +5y'-2y = 7t-5, y(0) = 0, y'(0) = 0, y"(0) = -2

A:

Q: x-64, y= 8t, -o<t< ∞

A:

Q: y""' + 2y" - 11y' - 12y = 11t - 9,y(0) = 0, y' (0) = 0, y"(0) = -3

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Q: y" + 7y' + 12y = 21 e3t, y(0) = 3.5, y'(0) = -10

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Q: (b) y" =-6y²y', with y(1) =1 and y'(1) =-2.

A:

Q: 3- y" - 2y3y = -3te-t

A: This is a non homogeneous differential equation. We solve the equation for homogeneous part then…

Q: y" - 4y' + 8y = x³, when x = 0, y = 2, y' = 4

A:

Q: (4x³y-$z+)(-2x-3 y7 z?) =D

A:

Q: . (D³ - D² - 4)y = 0

A:

Q: (D² - D - 2)y= 1-2x - 9e-2

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Q: Differentiate y' +y? - 5y - x? = -4

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Q: y"" + 3y" +3y' + y = 0, y(0) = 7, y'(0) =-7, y"(0) = 11

A:

Q: Find (a) c23 and (b) c32, where C = 5A + 2B,

A:

Q: 2y-9y+ 19= (y-5)

A: Given equation is: 2y2-9y+19=y-52 To solve for y.

Q: y" + 4y' + 5y = 35e-4x, y(0) = -2, y'(0) = 1

A: We are given the initial value program in which we have second order nonhomogeneous linear…

Q: - 4y - 25 > 2y + 17 What is y?

A:

Q: (D³ - 5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

A: The given differential equation is: D3-5D+4y=0 when x=0, y=-2, y'=8, y''=0.

Q: 4y" - 5y' = 0, y (-2) = 0 & y'(-2) = 7

A: Given differential equation is 4y''-5y'=0,  y-2=0  &amp;  y'-2=7

Q: When x = 12, y= 9.6. What is the value of y when x=20?

A:

Q: If y=3 then -y2=

A: Given Here the objective is to find the value of M

Q: 2) y/0 - 2y - 8y = 0

A: Given differential equation is. y4-2y''-8y=0 This can also be written as, D4-2D2-8y=0 where D≡ddx…

Q: (2x + 3)y' = y + √2x + 3, when x = -1, y = 0

A:

Q: y" - 10y' +9y = 5t, y(0) = -1 y' (0) = 2

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Q: y" - 4y' – 12y = 0, y(0) = – 1, y'(0) = 26

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Q: y" – 3y' + 2y = 4e2x, where y(0) = -3, y'(0) = 5

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Q: y" + 3y' = 0 y(0) = -2, y'(0) = 3

A: Given,            y''+3y'=0 , y0=-2 , y'0=3To find : The general solution of teh differential…

Q: -2 (3z') (3z")y z (2y²)(3y")z ) 21

A: We will find the solution.  We know  , let any number  x      If  (x)-2 = 1/ x2

Q: y' – 2y = y², when y = 3 and x |0 =

A: