Internal problem ID [4752]
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]
\[ \boxed {y^{2}+x y y^{\prime }=-1} \] 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 \left (x \right ) &= \frac {\sqrt {-x^{2}+25}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {-x^{2}+25}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.329 (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*}