77.1.69 problem 89 (page 123)

Internal problem ID [17959]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 89 (page 123)
Date solved : Tuesday, January 28, 2025 at 11:18:23 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 12

dsolve(diff(y(x),x)=y(x)*(ln(y(x)))^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 20

DSolve[D[y[x],x]==y[x]*(Log[y[x]])^2,y[x],x,IncludeSingularSolutions -> True]
 

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