What is the solution for y+sin(x)=x^3y^' ?

The solution for y+sin(x)=x^3y^' is y=(integral of \frac{sin(x)e^{1/(2x^2)})/(x^3)}{e^{1/(2x^2)}}

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y+sin(x)=x^3y^'

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

y = \frac{\int \frac{s i n ( x ) e ^{\frac{1}{2 x ^{2}}}}{x ^{3}} d x}{e ^{\frac{1}{2 x ^{2}}}}

Solution steps

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

Solve linear ODE:

y = \frac{\int \frac{s i n ( x ) e ^{\frac{1}{2 x ^{2}}}}{x ^{3}} d x}{e ^{\frac{1}{2 x ^{2}}}}

y = \frac{\int \frac{s i n ( x ) e ^{\frac{1}{2 x ^{2}}}}{x ^{3}} d x}{e ^{\frac{1}{2 x ^{2}}}}

\int e^{4 y} d y

x \to 0 + lim (x^{6 x})

s

\int 400 - x^{2} d x

What is the solution for y+sin(x)=x^3y^' ?
The solution for y+sin(x)=x^3y^' is y=(integral of \frac{sin(x)e^{1/(2x^2)})/(x^3)}{e^{1/(2x^2)}}