Internal problem ID [7943]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 363.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {\left (x y^{\prime }-y\right ) \left (\cos ^{2}\left (\frac {y}{x}\right )\right )+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.069 (sec). Leaf size: 35
dsolve((x*diff(y(x),x)-y(x))*cos(y(x)/x)^2+x = 0,y(x), singsol=all)
\[ -\frac {\cos \left (\frac {y \relax (x )}{x}\right ) \sin \left (\frac {y \relax (x )}{x}\right ) x +y \relax (x )}{2 x}-\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.265 (sec). Leaf size: 33
DSolve[x + Cos[y[x]/x]^2*(-y[x] + x*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)}{2 x}+\frac {1}{4} \sin \left (\frac {2 y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]