What is the solution for y^{''}-3y^'+2y=2t^2+e^t+1 ?

The solution for y^{''}-3y^'+2y=2t^2+e^t+1 is y=c_{1}e^{2t}+c_{2}e^t+t^2+3t-e^tt+4

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y^{''}-3y^'+2y=2t^2+e^t+1

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 t^{2} + e^{t} + 1

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{2} + 3 t - e^{t} t + 4

Solution steps

y^{''} (t) - 3 y^{'} (t) + 2 y = 2 t^{2} + e^{t} + 1

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{2} + 3 t - e^{t} t + 4

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{2} + 3 t - e^{t} t + 4

n = 3 \sum \infty \frac{n !}{2 ^{n + 1}}

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

\int 7 d x

x \to - \infty lim (\frac{- 3 x ^{3} - 4 x ^{2} + 2}{5 x ^{3} + 4 x ^{2} - 2 x})

What is the solution for y^{''}-3y^'+2y=2t^2+e^t+1 ?
The solution for y^{''}-3y^'+2y=2t^2+e^t+1 is y=c_{1}e^{2t}+c_{2}e^t+t^2+3t-e^tt+4