67.1.5 problem 2.2 (e)

Internal problem ID [16270]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (e)
Date solved : Thursday, October 02, 2025 at 10:45:10 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 42

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

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

✓ Sympy. Time used: 0.192 (sec). Leaf size: 26

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

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