What is the solution for y^{''}+3y^'-10y=6e^{4x} ?

The solution for y^{''}+3y^'-10y=6e^{4x} is y=c_{1}e^{2x}+c_{2}e^{-5x}+1/3 e^{4x}

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y^{''}+3y^'-10y=6e^{4x}

y^{^{''}} + 3 y^{^{'}} - 10 y = 6 e^{4 x}

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

Solution steps

y^{''} (x) + 3 y^{'} (x) - 10 y = 6 e^{4 x}

Solve linear ODE:

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

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

\int_{0}^{2} \frac{1}{16 + x ^{2}} d x

\int \frac{x}{x - 9} d x

4 x^{2} + 2 x - 1, at x = 0

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

\frac{30}{s ( s + 5 ) ( s + 4 )}

What is the solution for y^{''}+3y^'-10y=6e^{4x} ?
The solution for y^{''}+3y^'-10y=6e^{4x} is y=c_{1}e^{2x}+c_{2}e^{-5x}+1/3 e^{4x}