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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

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