What is the solution for y^'+3x^2y=sin(x)e^{-x^3} ?

The solution for y^'+3x^2y=sin(x)e^{-x^3} is y=-(cos(x))/(e^{x^3)}+(c_{1})/(e^{x^3)}

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y^'+3x^2y=sin(x)e^{-x^3}

y^{^{'}} + 3 x^{2} y = sin (x) e^{- x^{3}}

y = - \frac{cos ( x )}{e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

Solution steps

y^{'} (x) + 3 x^{2} y = sin (x) e^{- x^{3}}

Solve linear ODE:

y = - \frac{cos ( x )}{e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

y = - \frac{cos ( x )}{e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

x \to 3 lim (\frac{8 x + 7}{5 x + 7})

\frac{d}{d x} (\frac{1}{4} x^{4} + \frac{1}{8 x ^{2}})

\frac{d}{d x} (\frac{3}{x + 6})

\int e^{x} x - e^{x} + C d x

\frac{d}{d y} (y x)

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