Internal problem ID [2949]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 201.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x +x \left (\cos ^{2}\left (\frac {y}{x}\right )\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(x*diff(y(x),x) = y(x)-x*cos(y(x)/x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\arctan \left (c_{1}+\ln \relax (x )\right ) x \]
✓ Solution by Mathematica
Time used: 0.431 (sec). Leaf size: 37
DSolve[x y'[x]==y[x]-x Cos[y[x]/x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \text {ArcTan}(-\log (x)+2 c_1) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}