67.2.9 problem Problem 1(i)

Internal problem ID [13895]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(i)
Date solved : Monday, March 31, 2025 at 08:17:17 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\begin{align*} y &= \sqrt {2 x +c_1} \\ y &= -\sqrt {2 x +c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 38

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

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

✓ Sympy. Time used: 0.290 (sec). Leaf size: 22

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

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