What is the solution for y^'-2ty=9t^2e^{t^2} ?

The solution for y^'-2ty=9t^2e^{t^2} is y=3e^{t^2}t^3+c_{1}e^{t^2}

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y^'-2ty=9t^2e^{t^2}

y^{^{'}} - 2 t y = 9 t^{2} e^{t^{2}}

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

Solution steps

y^{'} (t) - 2 t y = 9 t^{2} e^{t^{2}}

Solve linear ODE:

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

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

What is the solution for y^'-2ty=9t^2e^{t^2} ?
The solution for y^'-2ty=9t^2e^{t^2} is y=3e^{t^2}t^3+c_{1}e^{t^2}