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

The solution for t^2y^{''}-2ty^'+2y=3t^2-t^3 is y=c_{1}t^2+c_{2}t+(-t^3+6t^2ln(t)-6t^2)/2

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

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

y = c_{1} t^{2} + c_{2} t + \frac{- t ^{3} + 6 t ^{2} ln ( t ) - 6 t ^{2}}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} t^{2} + c_{2} t + \frac{- t ^{3} + 6 t ^{2} ln ( t ) - 6 t ^{2}}{2}

y = c_{1} t^{2} + c_{2} t + \frac{- t ^{3} + 6 t ^{2} ln ( t ) - 6 t ^{2}}{2}

\int_{2}^{\infty} e^{- 7 p} d p

x \to - 2 lim (\frac{4}{x + 2})

\frac{d}{d x} (3 e^{- \frac{x}{4}})

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

What is the solution for t^2y^{''}-2ty^'+2y=3t^2-t^3 ?
The solution for t^2y^{''}-2ty^'+2y=3t^2-t^3 is y=c_{1}t^2+c_{2}t+(-t^3+6t^2ln(t)-6t^2)/2