60.1.525 problem 538

Internal problem ID [10539]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 538
Date solved : Sunday, March 30, 2025 at 05:48:52 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 2 \left (x y^{\prime }+y\right )^{3}-y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 3.147 (sec). Leaf size: 1724

ode:=2*(x*diff(y(x),x)+y(x))^3-y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 62.971 (sec). Leaf size: 96

ode=-(y[x]*D[y[x],x]) + 2*(y[x] + x*D[y[x],x])^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\int _1^x\frac {\text {InverseFunction}\left [\log (\text {$\#$1})+\frac {3 \sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}}{\text {$\#$1}}+\frac {2 \arctan \left (\sqrt {8 \text {$\#$1}-1}\right ) \text {$\#$1} \sqrt {8 \text {$\#$1}-1}}{\sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}}\&\right ][c_1+2 \log (K[1])]}{K[1]}dK[1]}{x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*(x*Derivative(y(x), x) + y(x))**3 - y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out