71.6.6 problem 6

Internal problem ID [14341]
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 : 6
Date solved : Monday, March 31, 2025 at 12:18:23 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Maple. Time used: 0.077 (sec). Leaf size: 13

ode:=diff(y(x),x) = 2*x/y(x); 
ic:=y(0) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \sqrt {2 x^{2}+4} \]

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 20

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

\[ y(x)\to \sqrt {2} \sqrt {x^2+2} \]

✓ Sympy. Time used: 0.280 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \sqrt {2 x^{2} + 4} \]