What is the solution for (dy)/(dt)-2ty=-9t^2e^{t^2} ?

The solution for (dy)/(dt)-2ty=-9t^2e^{t^2} is y=-3e^{t^2}t^3+c_{1}e^{t^2}

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(dy)/(dt)-2ty=-9t^2e^{t^2}

\frac{d y}{d t} - 2 t y = - 9 t^{2} e^{t^{2}}

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

Solution steps

\frac{d y}{d 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}}

\frac{d y}{d x} = 2 y^{2} + x y^{2}

\int \frac{1}{x ^{2} 2 + 9 x ^{2}} d x

\frac{\partial}{\partial y} ((x^{2} + y^{2}) ln (x^{2} + y^{2}))

5 t^{- \frac{3}{5}}

\frac{5}{3 - 2 x}

What is the solution for (dy)/(dt)-2ty=-9t^2e^{t^2} ?
The solution for (dy)/(dt)-2ty=-9t^2e^{t^2} is y=-3e^{t^2}t^3+c_{1}e^{t^2}