What is the solution for (dy)/(dx)-2xy=-6x^2e^{x^2} ?

The solution for (dy)/(dx)-2xy=-6x^2e^{x^2} is y=-2e^{x^2}x^3+c_{1}e^{x^2}

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(dy)/(dx)-2xy=-6x^2e^{x^2}

\frac{d y}{d x} - 2 x y = - 6 x^{2} e^{x^{2}}

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

Solution steps

\frac{d y}{d x} - 2 x y = - 6 x^{2} e^{x^{2}}

Solve linear ODE:

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

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

x \to 0 lim (\frac{sin ( c ) x}{x})

x \to 0 + lim (x^{x^{3}})

n = 1 \sum \infty \frac{( 1 ) ^{n}}{n}

n = 0 \sum \infty \frac{17}{2}

\frac{\partial}{\partial y} (e^{x y z^{2}} y z^{2})

What is the solution for (dy)/(dx)-2xy=-6x^2e^{x^2} ?
The solution for (dy)/(dx)-2xy=-6x^2e^{x^2} is y=-2e^{x^2}x^3+c_{1}e^{x^2}