32.6.2 problem Exercise 12.2, page 103

Internal problem ID [5867]
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
Date solved : Monday, January 27, 2025 at 01:21:42 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(cos(y(x))*diff(y(x),x)+sin(y(x))=x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\arcsin \left (-x^{2}+2 x -2+{\mathrm e}^{-x} c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 13.893 (sec). Leaf size: 23

DSolve[Cos[y[x]]*D[y[x],x]+Sin[y[x]]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (x^2-2 x-2 c_1 e^{-x}+2\right ) \]