1) . Solve the IVP:
y^''+6y^'+5y=0, y(0)=1, y^' (0)=3
2. Find the general solution to each of the following:
a) y^''+2y^'+5y=e^2x
b) y^''+2x/(x^2+1) y'=x
c) y^''+4y=1/(sin(2x)) (use variation of parameters)
6) a) Find the general solution to the 2nd order
differential equation
y''+6y'+8y=0
[8 pts]
b) Find the general solution to
y''+6y'+8y=2e-x.
Use the method of undetermined coefficients. [8
pts]
c) Solve the IVP
y''+6y'+8y=2e-x,
y0=0,
y'0=0
[5 pts]