Internal problem ID [4014]
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')`]
\[ \boxed {\cos \left (y\right ) y^{\prime }+\sin \left (y\right )-x^{2}=0} \]
✓ 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)
\[ y \left (x \right ) = \arcsin \left (\left ({\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}-c_{1} \right ) {\mathrm e}^{-x}\right ) \]
✓ Solution by Mathematica
Time used: 14.177 (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 \arcsin \left ((x-2) x-2 c_1 e^{-x}+2\right ) \\ \end{align*}