35.2.4 problem 4

Internal problem ID [6096]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 4
Date solved : Wednesday, March 05, 2025 at 12:12:23 AM
CAS classification : [_separable]

\begin{align*} 1+y^{2}+x y y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (5\right )&=0 \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 34

ode:=1+y(x)^2+x*y(x)*diff(y(x),x) = 0; 
ic:=y(5) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\begin{align*} y &= \frac {\sqrt {-x^{2}+25}}{x} \\ y &= -\frac {\sqrt {-x^{2}+25}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.358 (sec). Leaf size: 40

ode=(1+y[x]^2)+x*y[x]*D[y[x],x]==0; 
ic={y[5]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {\sqrt {25-x^2}}{x} \\ y(x)\to \frac {\sqrt {25-x^2}}{x} \\ \end{align*}

✓ Sympy. Time used: 0.531 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)*Derivative(y(x), x) + y(x)**2 + 1,0) 
ics = {y(5): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {-1 + \frac {25}{x^{2}}}, \ y{\left (x \right )} = \sqrt {-1 + \frac {25}{x^{2}}}\right ] \]