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

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

\frac{d}{d x} (\frac{2 x}{3 x ^{2} - 3})

t an g e n t f (x) = 6 x, at x = 9

\int 2 e^{x} x d x

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}