23.4.156 problem 156

Internal problem ID [6458]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 156
Date solved : Tuesday, September 30, 2025 at 02:57:29 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+a {y^{\prime }}^{2} \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 609

ode:=y(x)*diff(diff(y(x),x),x) = a0+a1*y(x)+a2*y(x)^2+a3*y(x)^2+a3*y(x)^3+a4*y(x)^4+a*diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 4.381 (sec). Leaf size: 1956

ode=y[x]*D[y[x],{x,2}] == a0 + a1*y[x] + a2*y[x]^2 + a3*y[x]^2 + a3*y[x]^3 + a4*y[x]^4 + a*D[y[x],x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
a0 = symbols("a0") 
a1 = symbols("a1") 
a2 = symbols("a2") 
a3 = symbols("a3") 
a4 = symbols("a4") 
y = Function("y") 
ode = Eq(-a*Derivative(y(x), x)**2 - a0 - a1*y(x) - a2*y(x)**2 - a3*y(x)**3 - a3*y(x)**2 - a4*y(x)**4 + y(x)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE sqrt(-(a0 + a1*y(x) + a2*y(x)**2 + a3*y(x)**3 + a3*y(x)**2 + a4*