Internal problem ID [4015]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.2, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {\cos \relax (y) y^{\prime }+\sin \relax (y)-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(cos(y(x))*diff(y(x),x)+sin(y(x))=x^2,y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\left ({\mathrm e}^{x} x^{2}-2 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-c_{1}\right ) {\mathrm e}^{-x}\right ) \]
✓ Solution by Mathematica
Time used: 16.043 (sec). Leaf size: 22
DSolve[Cos[y[x]]*y'[x]+Sin[y[x]]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcSin}\left ((x-2) x-2 c_1 e^{-x}+2\right ) \\ \end{align*}