Internal problem ID [5470]
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. Section 1.7. Homogeneous Equations. Page
28
Problem number: 7(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 36
dsolve(diff(y(x),x)=(x^2-x*y(x))/(y(x)^2*cos(x/y(x))),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2} \cos \left (\frac {1}{\textit {\_a}}\right )}{\textit {\_a}^{3} \cos \left (\frac {1}{\textit {\_a}}\right )+\textit {\_a} -1}d \textit {\_a} +\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 1.094 (sec). Leaf size: 49
DSolve[y'[x]==(x^2-x*y[x])/(y[x]^2*Cos[x/y[x]]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {\cos \left (\frac {1}{K[1]}\right ) K[1]^2}{\cos \left (\frac {1}{K[1]}\right ) K[1]^3+K[1]-1}dK[1]=-\log (x)+c_1,y(x)\right ] \]