23.2.281 problem 299

Internal problem ID [5636]
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 : 299
Date solved : Tuesday, September 30, 2025 at 01:21:11 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}+a_{0} {y^{\prime }}^{2}+a_{1} y^{\prime }+a_{2} +a_{3} y&=0 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 880

ode:=diff(y(x),x)^3+a__0*diff(y(x),x)^2+a__1*diff(y(x),x)+a__2+a__3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Mathematica

ode=(D[y[x],x])^3 + a0*(D[y[x],x])^2 +a1*D[y[x],x]+a2 +a3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
a1 = symbols("a1") 
a2 = symbols("a2") 
a3 = symbols("a3") 
y = Function("y") 
ode = Eq(a0*Derivative(y(x), x)**2 + a1*Derivative(y(x), x) + a2 + a3*y(x) + Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out