Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2...

Solve the initial value problem:

Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1

where f(t) { t if 0<=t<3 , t+2 if t>=3 }

Expert Solution

Colby Messinger answered 2 years ago

Solve the initial value problem: y'' + 4y' + 4y = 0; y(0) = 1, y'(0)...

Solve the initial value problem: y'' + 4y' + 4y = 0; y(0) = 1, y'(0) = 0. Solve without the Laplace Transform, first, and then with the Laplace Transform.

solve the following initial value problem y''+4y'=g(t),y(0)=0,y' (0)=1 if g(t) is the function which is 1...

solve the following initial value problem y''+4y'=g(t),y(0)=0,y' (0)=1 if g(t) is the function which is 1 on [0,1) and zero elsewhere

Solve the following initial value problem: y'''-4y''+20y'=-102e^3x, y(0)=3, y'(0)=-2, y''(0)=-2

(3 pts) Solve the initial value problem 25y′′−20y′+4y=0, y(5)=0, y′(5)=−e2. (3 pts) Solve the initial value...

(3 pts) Solve the initial value problem 25y′′−20y′+4y=0, y(5)=0, y′(5)=−e2. (3 pts) Solve the initial value problem y′′ − 2√2y′ + 2y = 0, y(√2) = e2, y′(√2) = 2√2e2. Consider the second order linear equation t2y′′+2ty′−2y=0, t>0. (a) (1 pt) Show that y1(t) = t−2 is a solution. (b) (3 pt) Use the variation of parameters method to obtain a second solution and a general solution.

use laplace transform to solve the initial value problem: y''+4y=3sint y(0)=1, y'(0)=-1

Solve the following differential equation: y''+4y'+4y=u(t-1)-u(t-3), y(0)=0, y'(0)=0

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

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

1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value...

1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value problem. yy'=e^x+x , y(0)=y_0 y_0 is a nonzero constant.

Solve the following initial value: y ''+ 4y = 2 cos 2t, y(0) = −2 and...

Solve the following initial value: y ''+ 4y = 2 cos 2t, y(0) = −2 and y 0 (0) = 0

Solve the laplace transform to solve the initial value problem. y"-6y'+9y=t. Y(0)=0, y'(0)=1

Question