What is the solution for x^{''}+3x^'-10x=6e^{4t} ?

The solution for x^{''}+3x^'-10x=6e^{4t} is x=c_{1}e^{2t}+c_{2}e^{-5t}+1/3 e^{4t}

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x^{''}+3x^'-10x=6e^{4t}

x^{^{''}} + 3 x^{^{'}} - 10 x = 6 e^{4 t}

x = c_{1} e^{2 t} + c_{2} e^{- 5 t} + \frac{1}{3} e^{4 t}

Solution steps

x^{''} (t) + 3 x^{'} (t) - 10 x = 6 e^{4 t}

Solve linear ODE:

x = c_{1} e^{2 t} + c_{2} e^{- 5 t} + \frac{1}{3} e^{4 t}

x = c_{1} e^{2 t} + c_{2} e^{- 5 t} + \frac{1}{3} e^{4 t}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 7 y = e^{5 x}

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 x

y^{^{''}} + y = \frac{1}{( sin ( x ) ) ^{3}}

(D^{2} - 4 D + 4) y = 8 e^{2 x} x^{2} sin (2 x)

x^{^{''}} - x = - 1

What is the solution for x^{''}+3x^'-10x=6e^{4t} ?
The solution for x^{''}+3x^'-10x=6e^{4t} is x=c_{1}e^{2t}+c_{2}e^{-5t}+1/3 e^{4t}