What is the solution for y^{''}-5y^'+6y=e^{6x} ?

The solution for y^{''}-5y^'+6y=e^{6x} is y=c_{1}e^{3x}+c_{2}e^{2x}+1/12 e^{6x}

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y^{''}-5y^'+6y=e^{6x}

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{6 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{1}{12} e^{6 x}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = e^{6 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{1}{12} e^{6 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{1}{12} e^{6 x}

\int sin (x) e^{x} d x

e^{5 t}

\int (x^{3} + 2)^{\frac{1}{2}} \cdot x^{2} d x

\frac{d}{d x} (sec^{2} (5 x^{2}))

What is the solution for y^{''}-5y^'+6y=e^{6x} ?
The solution for y^{''}-5y^'+6y=e^{6x} is y=c_{1}e^{3x}+c_{2}e^{2x}+1/12 e^{6x}