52.1.22 problem 22

Internal problem ID [10393]
Book : Second order enumerated odes
Section : section 1
Problem number : 22
Date solved : Tuesday, September 30, 2025 at 07:23:00 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✗ Maple

ode:=diff(diff(y(x),x),x)^2+diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(D[y[x],{x,2}])^2+D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2))**2