54.7.92 problem 1703 (book 6.112)

Internal problem ID [12941]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1703 (book 6.112)
Date solved : Wednesday, October 01, 2025 at 02:46:34 AM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime } y-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right )&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+exp(x)*y(x)*(c*y(x)^2+d)+exp(2*x)*(b+a*y(x)^4) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=E^x*y[x]*(d + c*y[x]^2) + E^(2*x)*(b + a*y[x]^4) - D[y[x],x]^2 + y[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
d = symbols("d") 
y = Function("y") 
ode = Eq((a*y(x)**4 + b)*exp(2*x) + (c*y(x)**2 + d)*y(x)*exp(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(a*y(x)**4*exp(2*x) + b*exp(2*x) + c*y(x)**3*exp(x) + d*y(x)*exp(x) + y(x)*Derivative(y(x), (x, 2))) + Derivative(y(x), x) cannot be solved by the factorable group method