Internal problem ID [8900]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 565.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_separable]
\[ \boxed {y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-y x=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 17
dsolve(y(x)*ln(diff(y(x),x))+diff(y(x),x)-y(x)*ln(y(x))-x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {\operatorname {LambertW}\left ({\mathrm e}^{x}\right ) \left (\operatorname {LambertW}\left ({\mathrm e}^{x}\right )+2\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 24
DSolve[-(x*y[x]) - Log[y[x]]*y[x] + Log[y'[x]]*y[x] + y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{\frac {1}{2} W\left (e^x\right ) \left (W\left (e^x\right )+2\right )} \]