Internal problem ID [6263]
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]
\[ \boxed {2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.766 (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)
\[ y \left (x \right ) = \arccos \left (\frac {\cos \left (1\right )}{x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 29.379 (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]
\[ y(x)\to \arccos \left (\frac {\cos (1)}{x^2}\right ) \]