Internal problem ID [5510]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Problems for Review and Discovery. Page
53
Problem number: 2(g).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 x \cos \relax (y)-x^{2} \sin \relax (y) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.531 (sec). Leaf size: 11
dsolve([2*x*cos(y(x))-x^2*sin(y(x))*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {\cos \relax (1)}{x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 36.657 (sec). Leaf size: 12
DSolve[{2*x*Cos[y[x]]-x^2*Sin[y[x]]*y'[x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec ^{-1}\left (x^2 \sec (1)\right ) \\ \end{align*}