79.6.4 problem (d)

Internal problem ID [21100]
Book : Ordinary Differential Equations. By Wolfgang Walter. Graduate texts in Mathematics. Springer. NY. QA372.W224 1998
Section : Chapter 1. First order equations: Some integrable cases. Excercises VIII at page 51
Problem number : (d)
Date solved : Thursday, October 02, 2025 at 07:08:17 PM
CAS classification : [_dAlembert]

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 76

ode:=y(x) = x*diff(y(x),x)^2+ln(diff(y(x),x)^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 \operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}} x +2 \,{\mathrm e}^{2 \textit {\_Z}} x +c_1 \,{\mathrm e}^{\textit {\_Z}}-2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}-2\right )} x +\ln \left ({\mathrm e}^{2 \operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}} x +2 \,{\mathrm e}^{2 \textit {\_Z}} x +c_1 \,{\mathrm e}^{\textit {\_Z}}-2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}-2\right )}\right ) \]

✓ Mathematica. Time used: 0.236 (sec). Leaf size: 53

ode=y[x]==x*D[y[x],x]^2+Log[D[y[x],x]^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=\frac {-\frac {2}{K[1]}-2 \log (K[1])}{(K[1]-1)^2}+\frac {c_1}{(K[1]-1)^2},y(x)=x K[1]^2+\log \left (K[1]^2\right )\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x)**2 + y(x) - log(Derivative(y(x), x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out