60.1.320 problem 326

Internal problem ID [10334]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 326
Date solved : Sunday, March 30, 2025 at 04:12:04 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.225 (sec). Leaf size: 160

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

\[ y = \frac {x \left (c_1 x -b \operatorname {RootOf}\left (b^{2} \textit {\_Z}^{4}-2 b x c_1 \,\textit {\_Z}^{3}+\left (a^{2} x^{2} c_1^{2}+b^{2} x^{2} c_1^{2}+x^{2} c_1^{2}-a^{2}\right ) \textit {\_Z}^{2}-2 b \,x^{3} c_1^{3} \textit {\_Z} +x^{4} c_1^{4}\right )\right )}{a \operatorname {RootOf}\left (b^{2} \textit {\_Z}^{4}-2 b x c_1 \,\textit {\_Z}^{3}+\left (a^{2} x^{2} c_1^{2}+b^{2} x^{2} c_1^{2}+x^{2} c_1^{2}-a^{2}\right ) \textit {\_Z}^{2}-2 b \,x^{3} c_1^{3} \textit {\_Z} +x^{4} c_1^{4}\right )} \]

✓ Mathematica. Time used: 0.248 (sec). Leaf size: 113

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1] \left (b^3+3 a K[1] b^2+3 a^2 K[1]^2 b+b+a^3 K[1]^3\right )}{(b+a K[1]) \left (a^2 K[1]^4+2 a b K[1]^3+a^2 K[1]^2+b^2 K[1]^2+K[1]^2+2 a b K[1]+b^2\right )}dK[1]=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out