77.1.98 problem 125 (page 179)

Internal problem ID [17988]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 125 (page 179)
Date solved : Tuesday, January 28, 2025 at 11:19:30 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 19

dsolve(y(x)*(1-ln(y(x)))*diff(y(x),x$2)+ (1+ln(y(x)))*diff(y(x),x)^2=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {c_{1} x +c_{2} -1}{c_{1} x +c_{2}}} \]

✓ Solution by Mathematica

Time used: 0.660 (sec). Leaf size: 34

DSolve[y[x]*(1-Log[y[x]])*D[y[x],{x,2}]+ (1+Log[y[x]])*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{\frac {c_1 x-1+c_2 c_1}{c_1 (x+c_2)}} \\ y(x)\to e \\ \end{align*}