15.19.21 problem 21

Internal problem ID [3305]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 21
Date solved : Sunday, March 30, 2025 at 01:34:15 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 53

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

\begin{align*} \frac {\left (2 y-2\right ) \sqrt {1-y}}{3}+x -c_1 +y-1 &= 0 \\ \frac {\left (-2 y+2\right ) \sqrt {1-y}}{3}+x -c_1 +y-1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 28.113 (sec). Leaf size: 1111

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out