8.3.20 problem 21

Internal problem ID [696]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 21
Date solved : Saturday, March 29, 2025 at 10:14:05 PM
CAS classification : [_separable]

\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \end{align*}

With initial conditions

\begin{align*} y \left (5\right )&=2 \end{align*}

✓ Maple. Time used: 0.111 (sec). Leaf size: 34

ode:=2*y(x)*diff(y(x),x) = x/(x^2-16)^(1/2); 
ic:=y(5) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\sqrt {\sqrt {x^{2}-16}\, \left (x^{2}+\sqrt {x^{2}-16}-16\right )}}{\sqrt {x^{2}-16}} \]

✓ Mathematica. Time used: 1.718 (sec). Leaf size: 20

ode=2*y[x]*D[y[x],x] == x/(x^2-16)^(1/2); 
ic=y[5]==2; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {\sqrt {x^2-16}+1} \]

✓ Sympy. Time used: 0.496 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x/sqrt(x**2 - 16) + 2*y(x)*Derivative(y(x), x),0) 
ics = {y(5): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {\sqrt {x^{2} - 16} + 1} \]