Internal problem ID [12204]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 56.
ODE order: 2.
ODE degree: 0.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(x*diff(y(x),x$2)=diff(y(x),x)*ln(diff(y(x),x)/x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{c_{1} x +1} c_{1} x +c_{2} c_{1}^{2}-{\mathrm e}^{c_{1} x +1}}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 0.905 (sec). Leaf size: 31
DSolve[x*y''[x]==y'[x]*Log[y'[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{e^{c_1} x+1-2 c_1} \left (-1+e^{c_1} x\right )+c_2 \]