What is the solution for (dy)/(dx)-2xy=-3x^2e^{x^2} ?

The solution for (dy)/(dx)-2xy=-3x^2e^{x^2} is y=-e^{x^2}x^3+c_{1}e^{x^2}

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(dy)/(dx)-2xy=-3x^2e^{x^2}

\frac{d y}{d x} - 2 x y = - 3 x^{2} e^{x^{2}}

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

Solution steps

\frac{d y}{d x} - 2 x y = - 3 x^{2} e^{x^{2}}

Solve linear ODE:

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

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

y \to 5 lim (\frac{25 - y ^{2}}{y ^{2} - 4 y - 5})

\int \frac{sin ( 2 t + 1 )}{cos ^{2} ( 2 t + 1 )} d t

y^{^{'}} = \frac{1 - x}{y}

\frac{d}{d x} (- 3 tan (3 x))

\frac{d}{d x} (- a sin (x))

What is the solution for (dy)/(dx)-2xy=-3x^2e^{x^2} ?
The solution for (dy)/(dx)-2xy=-3x^2e^{x^2} is y=-e^{x^2}x^3+c_{1}e^{x^2}