87.8.16 problem 16

Internal problem ID [23370]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 65
Problem number : 16
Date solved : Thursday, October 02, 2025 at 09:40:43 PM
CAS classification : [_quadrature]

\begin{align*} y y^{\prime }&=3 \end{align*}

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

ode:=y(x)*diff(y(x),x) = 3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {6 x +c_1} \\ y &= -\sqrt {6 x +c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 42

ode=y[x]*D[y[x],{x,1}]==3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {2} \sqrt {3 x+c_1}\\ y(x)&\to \sqrt {2} \sqrt {3 x+c_1} \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*Derivative(y(x), x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} + 6 x}, \ y{\left (x \right )} = \sqrt {C_{1} + 6 x}\right ] \]