Internal problem ID [4244]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {1+y^{2}+y y^{\prime } x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (5) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (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 \relax (x ) = \frac {\sqrt {-x^{2}+25}}{x} \\ y \relax (x ) = -\frac {\sqrt {-x^{2}+25}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.482 (sec). Leaf size: 40
DSolve[{(1+y[x]^2)+x*y[x]*y'[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*}