Internal problem ID [46]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 y y^{\prime }-\frac {x}{\sqrt {x^{2}-16}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (5) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.056 (sec). Leaf size: 34
dsolve([2*y(x)*diff(y(x),x) = x/(x^2-16)^(1/2),y(5) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {\sqrt {x^{2}-16}\, \left (x^{2}+\sqrt {x^{2}-16}-16\right )}}{\sqrt {x^{2}-16}} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 20
DSolve[{2*y[x]*y'[x] == x/(x^2-16)^(1/2),y[5]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {\sqrt {x^2-16}+1} \\ \end{align*}