60.1.515 problem 528

Internal problem ID [10529]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 528
Date solved : Sunday, March 30, 2025 at 05:45:16 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.042 (sec). Leaf size: 86

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

\[ y = -a x -\frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (-2 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+8 a \,{\mathrm e}^{\textit {\_Z}}+2 c_1 b -5 a^{2}-2 x b \right )}-a \right )^{2} {\mathrm e}^{\operatorname {RootOf}\left (-2 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+8 a \,{\mathrm e}^{\textit {\_Z}}+2 c_1 b -5 a^{2}-2 x b \right )}}{b} \]

✓ Mathematica. Time used: 0.146 (sec). Leaf size: 160

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

\[ \text {Solve}\left [\left \{x=\int _1^{\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{-2 a^3-27 b x a-27 b y(x)+\sqrt {\left (-2 a^3-27 b x a-27 b y(x)\right )^2-4 a^6}}}-\frac {a}{3}+\frac {\sqrt [3]{-2 a^3-27 b x a-27 b y(x)+\sqrt {\left (-2 a^3-27 b x a-27 b y(x)\right )^2-4 a^6}}}{3 \sqrt [3]{2}}}\frac {-3 K[1]^2-2 a K[1]}{b (a+K[1])}dK[1]+c_1\right \},y(x)\right ] \]

✗ Sympy

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

Timed Out