77.1.154 problem 181 (page 297)

Internal problem ID [17973]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 181 (page 297)
Date solved : Monday, March 31, 2025 at 04:52:54 PM
CAS classification : [[_2nd_order, _missing_x], [_Emden, _modified]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x)^2 = 0; 
ic:=y(0) = 1, D(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]+2*D[y[x],x]+y[x]^2==0; 
ic={y[0]==1,Derivative[1][y][0] == 0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE y(x)**2/2 + Derivative(y(x), x) + Derivative(y(x), (x, 2))/2 cannot be solved by the factorable group method