75.8.14 problem 212

Internal problem ID [16830]
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
Date solved : Tuesday, January 28, 2025 at 09:34:12 AM
CAS classification : [_quadrature]

\begin{align*} y&=y^{\prime } \ln \left (y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 63

dsolve(y(x)=diff(y(x),x)*ln(diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y &= \left (-1-\sqrt {1+2 x -2 c_{1}}\right ) {\mathrm e}^{-1-\sqrt {1+2 x -2 c_{1}}} \\ y &= \left (-1+\sqrt {1+2 x -2 c_{1}}\right ) {\mathrm e}^{-1+\sqrt {1+2 x -2 c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 27

DSolve[y[x]==D[y[x],x]*Log[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {W(K[1])}{K[1]}dK[1]\&\right ][x+c_1] \]