1. Find the general solution of the differential equations.
   • \( y''-3y'+2y=5e^{3t} \) View Solution
   • \( y''-3y'+2y=5e^{t} \) View Solution
   • \( y''+2y'-3y=10e^{-3t} \) View Solution (PDF)
   • \( y''+4y=\sin(2t) \) View Solution
   • \( y''+4y'+4y=3t^2-1 \) View Solution
2. SET UP the correct form for the particular solution, \( y_p(t) \). DO NOT solve for the coefficients.
   • \( y''-3y'+2y=5e^{t}+3t \) View Solution
   • \( y''-3y'=\cosh(3t)-5 \) View Solution
   • \( y''+4y=e^{2t}\sin(2t) \) View Solution
   • \( y''+5y'-6y=3^{-t} \) View Solution (Note: \(3^{-t} = e^{(-\ln 3) t}\))
   • \( y''- (\ln 2)y'=2^t \) View Solution
   • \( y''-y'-2y=\cosh (2t) \) View Solution
   • \( y''-6y'+58y=t^2e^t \cos 2t \) View Solution
   • \( y''-10y'+25y=\cos 3t + t\, e^{5t} \) View Solution
3. Find the solution of the given initial value problem (IVP).
   • \( y''+ y'- 2y= 2t, \quad y(0)=0, \: y'(0)=1 \) View Solution
   • \( y''+4y=3\cos(2t), \quad y(0)=2, \: y'(0)=-1 \) View Solution