71.6.11 problem 11

Internal problem ID [14346]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 11
Date solved : Monday, March 31, 2025 at 12:18:41 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

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

\begin{align*} y &= \sqrt {x +c_1} \\ y &= -\sqrt {x +c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 31

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

\begin{align*} y(x)\to -\sqrt {x+2 c_1} \\ y(x)\to \sqrt {x+2 c_1} \\ \end{align*}

✓ Sympy. Time used: 0.285 (sec). Leaf size: 19

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} + x}, \ y{\left (x \right )} = \sqrt {C_{1} + x}\right ] \]