89.32.21 problem 24

Internal problem ID [24981]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Miscellaneous Exercises at page 246
Problem number : 24
Date solved : Thursday, October 02, 2025 at 11:45:18 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.092 (sec). Leaf size: 56

ode:=diff(y(x),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 {x}{3}-\frac {2}{27}-\frac {2 \sqrt {-\left (3 x -1\right )^{3}}}{27} \\ y &= \frac {x}{3}-\frac {2}{27}+\frac {2 \sqrt {-\left (3 x -1\right )^{3}}}{27} \\ y &= c_1 \left (c_1^{2}-c_1 +x \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 74

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

\begin{align*} y(x)&\to c_1 (x+(-1+c_1) c_1)\\ y(x)&\to \frac {1}{27} \left (9 x-2 \left (\sqrt {-(3 x-1)^3}+1\right )\right )\\ y(x)&\to \frac {1}{27} \left (9 x+2 \sqrt {-(3 x-1)^3}-2\right ) \end{align*}

✗ Sympy

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

Timed Out