What is the solution for y^{''}-5y^'+6y=e^t ?

The solution for y^{''}-5y^'+6y=e^t is y=c_{1}e^{3t}+c_{2}e^{2t}+1/2 e^t

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y^{''}-5y^'+6y=e^t

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{t}

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

Solution steps

y^{''} (t) - 5 y^{'} (t) + 6 y = e^{t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

\int_{0}^{1} 9 t^{4} + 4 t^{2} d t

\int_{1}^{4} (x^{2} + x) d x

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

\int e^{x} - 1 d x

\frac{d}{d x} (x^{4} - 8 x^{2})

What is the solution for y^{''}-5y^'+6y=e^t ?
The solution for y^{''}-5y^'+6y=e^t is y=c_{1}e^{3t}+c_{2}e^{2t}+1/2 e^t