1. Solve the initial value problems a.) y"-10y'+25y=e^5x, y(0)= 1 and y'(0)= 6 b.) y"+y'-2y=2sin(x), y(0)=...

1. Solve the initial value problems

a.) y"-10y'+25y=e^5x, y(0)= 1 and y'(0)= 6

b.) y"+y'-2y=2sin(x), y(0)= 1 and y'(0)= 2

c.) y"+14y'+49y=0, y(0)= -1 and y'(0)= 9

2. Find a two-parameter family of solutions to the following differential equations

a.) y"-3y'-10y=14e^-2x

b.) y"-6y'+25y=0

Expert Solution

milcah answered 2 years ago

Solve the following initial value problem. y′′ − 10y′ + 24y = 5x + e^(4x), y(0) ...

Solve the following initial value problem. y′′ − 10y′ + 24y = 5x + e^(4x), y(0) = 0, y′(0) = 4 (not using Laplace)

Solve the given initial value problem. y'''+2y''-13y'+10y=0 y(0)=4 y'(0)=42 y''(0)= -134 y(x)=

Use power series to solve the initial value problem x^2y''+xy'+x^2y=0, y(0)=1, y'(0)=0

Solve the system by Laplace Transform: x'=x-2y y'=5x-y x(0)=-1, y(0)=2

Solve the initial value problem: y''+2y'+y = x^2 , y(0)=0 , y'(0) = 0

Solve the initial–value problem by using the Laplace transform. y′′ +2y′ +10y = δ(t−π), y(0) =...

Solve the initial–value problem by using the Laplace transform. y′′ +2y′ +10y = δ(t−π), y(0) = 0, y′(0) = 4

Solve the following IVPs: A. y"" +2y′′+y = 4et, y(0)=1, y′(0)=1, y′′(0)=1, y′′′(0)=1. B. y′′′+25y′ = 325e−t,...

Solve the following IVPs: A. y"" +2y′′+y = 4et, y(0)=1, y′(0)=1, y′′(0)=1, y′′′(0)=1. B. y′′′+25y′ = 325e−t, y(0) = 0, y′(0) = 0, y′′(0) = 0.

Use the Laplace transform to solve the given initial value problem. y'' + 2y' + 10y...

Use the Laplace transform to solve the given initial value problem. y'' + 2y' + 10y = 6cos2t - 4sin2t, y(0)=2, y'(0)= -2

Solve the following initial value problems y'' + y = 2/cos x , y(0) = y'(0)...

Solve the following initial value problems y'' + y = 2/cos x , y(0) = y'(0) = 2 x^3 y''' − 6xy' + 12y = 20x^4, x > 0, y(1) = 8/3 , y'(1) = 50/3 , y''(1) = 14 x^2 y'' − 2xy' + 2y = x^2, x > 0, y(1) = 3, y'(1) = 5

solve the initial value problem Y" + 2Y' - Y = 0, Y(0)=0,Y'(0) = 2sqrt2

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