What is the solution for y^{''}-11y^'+30y=20e^t ?

The solution for y^{''}-11y^'+30y=20e^t is y=c_{1}e^{6t}+c_{2}e^{5t}+e^t

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y^{''}-11y^'+30y=20e^t

y^{^{''}} - 11 y^{^{'}} + 30 y = 20 e^{t}

y = c_{1} e^{6 t} + c_{2} e^{5 t} + e^{t}

Solution steps

y^{''} (t) - 11 y^{'} (t) + 30 y = 20 e^{t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{5 t} + e^{t}

y = c_{1} e^{6 t} + c_{2} e^{5 t} + e^{t}

\int_{0}^{2} (sin (x) + e^{x}) d x

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

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 6}{x})

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

\int \frac{29 x ^{4} + 29 x ^{3} + 2 x + 1}{x ^{2} + x} d x

What is the solution for y^{''}-11y^'+30y=20e^t ?
The solution for y^{''}-11y^'+30y=20e^t is y=c_{1}e^{6t}+c_{2}e^{5t}+e^t