[tex](y + \sin y)y'= x + x^3 \\
\Rightarrow (y + \sin y)\dfrac{dy}{dx}= x + x^3 \\
\Rightarrow (y + \sin y)dy= \left( x + x^3\right)dx \\
\Rightarrow \displaystyle\int(y + \sin y)dy= \int \left( x + x^3\right)dx \\ \\
\Rightarrow \dfrac{y^2}{2} - \cos y = \dfrac{x^2}{2} + \dfrac{x^4}{4} + C[/tex]
It is [tex]\dfrac{y^2}{2} - \cos y = \dfrac{x^2}{2} + \dfrac{x^4}{4} + C[/tex] as you cannot simplify further
