23.2.271 problem 286

Internal problem ID [5626]
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 : 286
Date solved : Tuesday, September 30, 2025 at 01:14:28 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.128 (sec). Leaf size: 65

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 72

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

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

✗ Sympy

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

Timed Out