Second order non-homogeneous linear diff equations:
1. Find the general solution of the diff equations.
a. \( y''-3y'+2y=5e^{3t} \)
solution
b. \( y''-3y'+2y=5e^{t} \)
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c. \( y''+2y'-3y=10e^{-3t} \)
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d. \( y''+4y=\sin(2t) \)
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e. \( y''+4y'+4y=3t^2-1 \)
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2. SET UP the correct form for the particular solution, \( y_p(t)\).
DO NOT solve for the coefficients.
a. \( y''-3y'+2y=5e^{t}+3t \)
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b. \( y''-3y'=\cosh(3t)-5 \)
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c. \( y''+4y=e^{2t}\sin(2t) \)
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d. \( y''+5y'-6y=3^{-t} \)
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(Note: \(3^{-t} = e^{(-\ln 3) t}\))
e. \( y''- (\ln 2)y'=2^t \)
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f. \( y''-y'-2y=\cosh (2t) \)
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g. \( y''-6y'+58y=t^2e^t \cos 2t\)
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h. \( y''-10y'+25y=\cos 3t + t\, e^{5t}\)
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3. Find the solution of the given initial value problem.
a. \( y''+ y'- 2y= 2t, \quad y(0)=0,
\:
y'(0)=1 \) solution
b. \( y''+4y=3\cos(2t), \quad
y(0)=2, \: y'(0)=-1 \)
solution