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{\partial}{\partial x} (2 y x^{2} - 4)

\int_{2}^{\infty} \frac{1}{3 x} d x

r^{2} - 13 x^{2}

y^{^{'}} = 3 - 2 x - 0.5 y, y (0) = 1

\frac{d}{d x} ((ln (x))^{s e c (x)})

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}