Internal problem ID [7926]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 346.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x \left (y \ln \left (y x \right )+y-a x \right ) y^{\prime }-y \left (a x \ln \left (y x \right )-y+a x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(x*(y(x)*ln(x*y(x))+y(x)-a*x)*diff(y(x),x)-y(x)*(a*x*ln(x*y(x))-y(x)+a*x) = 0,y(x), singsol=all)
\[ \left (x y \relax (x )\right )^{-a x +y \relax (x )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 24
DSolve[-((a*x + a*x*Log[x*y[x]] - y[x])*y[x]) + x*(-(a*x) + y[x] + Log[x*y[x]]*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[a x \log (x y(x))-y(x) \log (x y(x))=c_1,y(x)] \]