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
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.