23.2.280 problem 298

Internal problem ID [5635]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 298
Date solved : Tuesday, September 30, 2025 at 01:20:27 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: 0.046 (sec). Leaf size: 90

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);
 

\[ y = -a x -\frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (-10 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+16 a \,{\mathrm e}^{\textit {\_Z}}+2 c_1 b -13 a^{2}-2 x b \right )}-a \right )^{2} \left (-2 a +{\mathrm e}^{\operatorname {RootOf}\left (-10 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+16 a \,{\mathrm e}^{\textit {\_Z}}+2 c_1 b -13 a^{2}-2 x b \right )}\right )}{b} \]

✓ Mathematica. Time used: 0.095 (sec). Leaf size: 160

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

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

✗ 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