54.1.404 problem 415

Internal problem ID [11718]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 415
Date solved : Tuesday, September 30, 2025 at 10:14:17 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \end{align*}

✓ Maple. Time used: 0.136 (sec). Leaf size: 89

ode:=x*diff(y(x),x)^2+y(x)*diff(y(x),x)-y(x)^4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {1}{2 \sqrt {-x}} \\ y &= \frac {1}{2 \sqrt {-x}} \\ y &= 0 \\ y &= -\frac {\sqrt {x \operatorname {sech}\left (-\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )^{2}}\, \coth \left (-\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )}{2 x} \\ y &= \frac {\sqrt {x \operatorname {sech}\left (-\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )^{2}}\, \coth \left (-\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.249 (sec). Leaf size: 84

ode=-y[x]^4 + y[x]*D[y[x],x] + x*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {2 e^{\frac {c_1}{2}}}{-4 x+e^{c_1}}\\ y(x)&\to \frac {2 e^{\frac {c_1}{2}}}{-4 x+e^{c_1}}\\ y(x)&\to 0\\ y(x)&\to -\frac {i}{2 \sqrt {x}}\\ y(x)&\to \frac {i}{2 \sqrt {x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x)**2 - y(x)**4 + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out