40.14.15 problem 36

Internal problem ID [6786]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 36
Date solved : Sunday, March 30, 2025 at 11:22:41 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} 2 \left (y+1\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y&=0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 41

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

\begin{align*} y &= -1-\sqrt {1+2 c_2 \cos \left (x \right )-2 c_1 \sin \left (x \right )} \\ y &= -1+\sqrt {1+2 c_2 \cos \left (x \right )-2 c_1 \sin \left (x \right )} \\ \end{align*}

✓ Mathematica. Time used: 25.02 (sec). Leaf size: 5629

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

Too large to display

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(-2*y(x)**2 - 4*y(x)*Derivative(y(x), (x, 2)) - 4*y(x) - 4*Derivative(y(x), (x, 2)))/2 + Derivative(y(x), x) cannot be solved by the factorable group method