23.2.63 problem 65

Internal problem ID [5418]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 65
Date solved : Tuesday, September 30, 2025 at 12:40:59 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.971 (sec). Leaf size: 143

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

\begin{align*} x +\frac {3 \ln \left (y-1\right )}{2}-\frac {\ln \left (y\right )}{2}+\frac {\ln \left (\sqrt {8 y+1}-1\right )}{2}-\frac {3 \ln \left (\sqrt {8 y+1}-3\right )}{2}-\frac {\ln \left (\sqrt {8 y+1}+1\right )}{2}+\frac {3 \ln \left (\sqrt {8 y+1}+3\right )}{2}-c_1 &= 0 \\ x +\frac {3 \ln \left (y-1\right )}{2}-\frac {\ln \left (y\right )}{2}-\frac {\ln \left (\sqrt {8 y+1}-1\right )}{2}+\frac {3 \ln \left (\sqrt {8 y+1}-3\right )}{2}+\frac {\ln \left (\sqrt {8 y+1}+1\right )}{2}-\frac {3 \ln \left (\sqrt {8 y+1}+3\right )}{2}-c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 60.076 (sec). Leaf size: 1373

ode=(D[y[x],x])^2+(1+2*y[x])*D[y[x],x]+y[x]*(y[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) - 1)*y(x) + (2*y(x) + 1)*Derivative(y(x), x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out