What is the solution for y^'+6xy=x^4e^{(-6x^2)/2} ?

The solution for y^'+6xy=x^4e^{(-6x^2)/2} is y=(x^5)/(5e^{3x^2)}+(c_{1})/(e^{3x^2)}

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y^'+6xy=x^4e^{(-6x^2)/2}

y^{^{'}} + 6 x y = x^{4} e^{\frac{- 6 x ^{2}}{2}}

y = \frac{x ^{5}}{5 e ^{3 x^{2}}} + \frac{c _{1}}{e ^{3 x^{2}}}

Solution steps

y^{'} (x) + 6 x y = x^{4} e^{\frac{- 6 x ^{2}}{2}}

Solve linear ODE:

y = \frac{x ^{5}}{5 e ^{3 x^{2}}} + \frac{c _{1}}{e ^{3 x^{2}}}

y = \frac{x ^{5}}{5 e ^{3 x^{2}}} + \frac{c _{1}}{e ^{3 x^{2}}}

\int 2 sin^{3} (x) \cdot cos^{2} (x) d x

\int cos^{4} (2 x) d x

\frac{d}{d x} (2 x^{3} + 6 x - 2)

\frac{\partial}{\partial u} (uv)

\frac{d y}{d x}, y = x^{x}

What is the solution for y^'+6xy=x^4e^{(-6x^2)/2} ?
The solution for y^'+6xy=x^4e^{(-6x^2)/2} is y=(x^5)/(5e^{3x^2)}+(c_{1})/(e^{3x^2)}