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} = y sin (x), y (0) = 1

\int e^{x y} d x

f (x) = \frac{1 + 16 x ^{2}}{( 4 x ) ^{3}}

y^{^{''}} - y^{^{'}} = 0, y (0) = 10

\int \frac{4}{3 - x} d 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}