60.1.509 problem 522

Internal problem ID [10523]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 522
Date solved : Sunday, March 30, 2025 at 05:43:06 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.098 (sec). Leaf size: 44

ode:=diff(y(x),x)^3-(x+5)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {2 \sqrt {3 x +15}\, \left (x +5\right )}{9} \\ y &= \frac {2 \sqrt {3 x +15}\, \left (x +5\right )}{9} \\ y &= c_1 \left (-c_1^{2}+x +5\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 57

ode=y[x] - (5 + x)*D[y[x],x] + D[y[x],x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 \left (x+5-c_1{}^2\right ) \\ y(x)\to -\frac {2 (x+5)^{3/2}}{3 \sqrt {3}} \\ y(x)\to \frac {2 (x+5)^{3/2}}{3 \sqrt {3}} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x - 5)*Derivative(y(x), x) + y(x) + Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out