What is the solution for x^{''}-3x^'=e^{3t} ?

The solution for x^{''}-3x^'=e^{3t} is x=c_{1}e^{3t}+c_{2}+(e^{3t}t)/3

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x^{''}-3x^'=e^{3t}

x^{^{''}} - 3 x^{^{'}} = e^{3 t}

x = c_{1} e^{3 t} + c_{2} + \frac{e ^{3 t} t}{3}

Solution steps

x^{''} (t) - 3 x^{'} (t) = e^{3 t}

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} + \frac{e ^{3 t} t}{3}

x = c_{1} e^{3 t} + c_{2} + \frac{e ^{3 t} t}{3}

2 cos (x), 4 - 2 cos (x)

\int sin (yz) d y

\frac{d}{d x} (ln^{2} (x))

f (x) = - \frac{7}{x ^{8}}

\frac{d}{d x} ((x + y)^{3})

What is the solution for x^{''}-3x^'=e^{3t} ?
The solution for x^{''}-3x^'=e^{3t} is x=c_{1}e^{3t}+c_{2}+(e^{3t}t)/3