Internal problem ID [7942]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 362.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {\left (x^{2} y \sin \left (y x \right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (y x \right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.306 (sec). Leaf size: 22
dsolve((x^2*y(x)*sin(x*y(x))-4*x)*diff(y(x),x)+x*y(x)^2*sin(x*y(x))-y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (\textit {\_Z} -{\mathrm e}^{-\frac {\cos \left (\textit {\_Z} \right )}{4}} c_{1} x^{\frac {3}{4}}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.259 (sec). Leaf size: 23
DSolve[-y[x] + x*Sin[x*y[x]]*y[x]^2 + (-4*x + x^2*Sin[x*y[x]]*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[-4 \log (y(x))-\cos (x y(x))-\log (x)=c_1,y(x)] \]