54.1.528 problem 541

Internal problem ID [11842]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 541
Date solved : Tuesday, September 30, 2025 at 11:21:35 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.272 (sec). Leaf size: 95

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

\begin{align*} y &= -\frac {2 \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= \frac {2 \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= -\frac {2 i \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= \frac {2 i \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= 0 \\ y &= \sqrt {c_1 \left (c_1^{2}+2 x \right )} \\ y &= -\sqrt {c_1 \left (c_1^{2}+2 x \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 119

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

\begin{align*} y(x)&\to -\sqrt {2 c_1 x+c_1{}^3}\\ y(x)&\to \sqrt {2 c_1 x+c_1{}^3}\\ y(x)&\to (-1-i) \left (\frac {2}{3}\right )^{3/4} x^{3/4}\\ y(x)&\to (1-i) \left (\frac {2}{3}\right )^{3/4} x^{3/4}\\ y(x)&\to (-1+i) \left (\frac {2}{3}\right )^{3/4} x^{3/4}\\ y(x)&\to (1+i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} \end{align*}

✗ Sympy

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

IndexError : list index out of range