Internal problem ID [4246]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x y^{2}+x}{x^{2} y-y}=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\sqrt {2}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 31
dsolve([diff(y(x),x)=(2*x*y(x)^2+x)/(x^2*y(x)-y(x)),y(2^(1/2)) = 0],y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {2 x^{2}-4}\, x}{2} \\ y \relax (x ) = \frac {\sqrt {2 x^{2}-4}\, x}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.24 (sec). Leaf size: 48
DSolve[{y'[x]==(2*x*y[x]^2+x)/(x^2*y[x]-y[x]),{y[Sqrt[2]]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2 \left (x^2-2\right )}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {x^2 \left (x^2-2\right )}}{\sqrt {2}} \\ \end{align*}