What is the solution for y^{''}-3y^'+2y=2e^3t ?

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

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y^{''}-3y^'+2y=2e^3t

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{3} t

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

Solution steps

y^{''} (t) - 3 y^{'} (t) + 2 y = 2 e^{3} t

Solve linear ODE:

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

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

x \to \infty lim (\frac{8}{x})

(- 1, 3), (13, 1)

\int \frac{tan ( x )}{cos ^{2} ( x )} d x

8 t \frac{d y}{d t} + y = t^{4}

\frac{\partial}{\partial y} (x + x^{2} + y^{2})

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