Internal problem ID [7942]
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]
\[ \boxed {\left (y^{\prime } x -y\right ) \cos \left (\frac {y}{x}\right )^{2}+x=0} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 35
dsolve((x*diff(y(x),x)-y(x))*cos(y(x)/x)^2+x = 0,y(x), singsol=all)
\[ -\frac {\cos \left (\frac {y \left (x \right )}{x}\right ) \sin \left (\frac {y \left (x \right )}{x}\right ) x +y \left (x \right )}{2 x}-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.271 (sec). Leaf size: 33
DSolve[x + Cos[y[x]/x]^2*(-y[x] + x*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)}{2 x}+\frac {1}{4} \sin \left (\frac {2 y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]