Differential Equations Answers

(D+2)x-3y=1

-3x+(D+2)y=e^-t

y"+3y'+2y=e^(-t) , y(0)=0, y'(0)=0

Determine the unique solution of the following differential equations by using Laplace transforms:

y''(t) + 2y'(t) -3y(t) = e^-3t if y'(0) = 0 and y(0) = 0

Determine the unique solution of the following differential equations by using Laplace transforms:

y''(t)-6y'(t)+9y(t) = t²e^3t if y'(0) = 6 and y(0) = 2

Determine L^-1{e^s(s²-1/(s²+1)²)}

Find the general solutions of the following differential equations using D-operator methods:

2.1 (D² - 2D + 5)y = x+5

2.2 (D+4)² x = sinh4t

The expression that is equivalent to (a3b2)3 is