23.2.177 problem 181

Internal problem ID [5532]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 181
Date solved : Tuesday, September 30, 2025 at 12:51:25 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 1.839 (sec). Leaf size: 141

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

\begin{align*} y &= \frac {\operatorname {RootOf}\left (-4 \ln \left (x \right )+4 c_1 +3 \ln \left (-2+\textit {\_Z} \right )+\ln \left (\textit {\_Z} \right )+\ln \left (-1+\sqrt {4 \textit {\_Z} +1}\right )-\ln \left (1+\sqrt {4 \textit {\_Z} +1}\right )-3 \ln \left (\sqrt {4 \textit {\_Z} +1}-3\right )+3 \ln \left (\sqrt {4 \textit {\_Z} +1}+3\right )\right )}{x} \\ y &= \frac {\operatorname {RootOf}\left (-4 \ln \left (x \right )+4 c_1 +3 \ln \left (-2+\textit {\_Z} \right )+\ln \left (\textit {\_Z} \right )-\ln \left (-1+\sqrt {4 \textit {\_Z} +1}\right )+\ln \left (1+\sqrt {4 \textit {\_Z} +1}\right )+3 \ln \left (\sqrt {4 \textit {\_Z} +1}-3\right )-3 \ln \left (\sqrt {4 \textit {\_Z} +1}+3\right )\right )}{x} \\ \end{align*}

✓ Mathematica. Time used: 63.652 (sec). Leaf size: 4335

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

Too large to display

✗ Sympy

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

Timed Out