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 : Monday, January 27, 2025 at 01:35:57 PM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[{(1+y[x]^2)+x*y[x]*D[y[x],x]==0,{y[5]==0}},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*}