23.4.134 problem 134

Internal problem ID [6436]
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 : 134
Date solved : Tuesday, September 30, 2025 at 02:56:49 PM
CAS classification : [NONE]

\begin{align*} y y^{\prime \prime }&={\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2} \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ 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 + a1*y(x)**2)*y(x)*exp(x) - (a2 + a3*y(x)**4)*exp(2*x) + y(x)*Derivative(y(x), (x, 2)) - Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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