23.2.24 problem 25

Internal problem ID [5379]
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 : 25
Date solved : Tuesday, September 30, 2025 at 12:38:26 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 45

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

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

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 47

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

\begin{align*} y(x)&\to -\frac {2}{3} (1-x)^{3/2}-x+c_1\\ y(x)&\to \frac {2}{3} (1-x)^{3/2}-x+c_1 \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 31

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

\[ \left [ y{\left (x \right )} = C_{1} - x + \frac {2 \left (1 - x\right )^{\frac {3}{2}}}{3}, \ y{\left (x \right )} = C_{1} - x - \frac {2 \left (1 - x\right )^{\frac {3}{2}}}{3}\right ] \]