Internal problem ID [15100]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 212.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-y^{\prime } \ln \left (y^{\prime }\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(y(x)=diff(y(x),x)*ln(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (-1-\sqrt {1-2 c_{1} +2 x}\right ) {\mathrm e}^{-1-\sqrt {1-2 c_{1} +2 x}} \\ y \left (x \right ) &= \left (-1+\sqrt {1-2 c_{1} +2 x}\right ) {\mathrm e}^{-1+\sqrt {1-2 c_{1} +2 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.166 (sec). Leaf size: 83
DSolve[y[x]==y'[x]*Log[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{-1-\sqrt {2 x+1+2 c_1}} \left (1+\sqrt {2 x+1+2 c_1}\right ) \\ y(x)\to e^{-1+\sqrt {2 x+1+2 c_1}} \left (-1+\sqrt {2 x+1+2 c_1}\right ) \\ y(x)\to 0 \\ \end{align*}