60.1.549 problem 562

Internal problem ID [10563]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 562
Date solved : Sunday, March 30, 2025 at 06:05:55 PM
CAS classification : [_dAlembert]

\begin{align*} a \left ({y^{\prime }}^{3}+1\right )^{{1}/{3}}+b x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.221 (sec). Leaf size: 3313

ode:=a*(diff(y(x),x)^3+1)^(1/3)+b*x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 84

ode=-y[x] + b*x*D[y[x],x] + a*(1 + D[y[x],x]^3)^(1/3)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=K[1]^{\frac {b}{1-b}} \left (\frac {a \int \frac {K[1]^{\frac {2 b-1}{b-1}}}{\left (K[1]^3+1\right )^{2/3}}dK[1]}{1-b}+c_1\right ),y(x)=a \sqrt [3]{K[1]^3+1}+b x K[1]\right \},\{K[1],y(x)\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(a*(Derivative(y(x), x)**3 + 1)**(1/3) + b*x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out