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

The solution for y^{''}-3y^'+2y=2t^3 is y=c_{1}e^{2t}+c_{2}e^t+t^3+(9t^2)/2+(21t)/2+45/4

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

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

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{3} + \frac{9 t ^{2}}{2} + \frac{21 t}{2} + \frac{45}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{3} + \frac{9 t ^{2}}{2} + \frac{21 t}{2} + \frac{45}{4}

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{3} + \frac{9 t ^{2}}{2} + \frac{21 t}{2} + \frac{45}{4}

\frac{d}{d x} (ln (x^{4} - 6 x^{2}))

\int tan^{3} (21 π x) d x

g (x) = \frac{sin ( 8 x )}{cos ( x )}

\int_{1}^{\infty} - \frac{1}{x} d x

(cos (3 x)) y^{^{'}} - 3 (tan (3 x)) y = - 10 sec (3 x)

What is the solution for y^{''}-3y^'+2y=2t^3 ?
The solution for y^{''}-3y^'+2y=2t^3 is y=c_{1}e^{2t}+c_{2}e^t+t^3+(9t^2)/2+(21t)/2+45/4