35.2.6 problem 6

Internal problem ID [6098]
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
Date solved : Monday, January 27, 2025 at 01:36:02 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\sqrt {2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (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 &= -\frac {\sqrt {2 x^{2}-4}\, x}{2} \\ y &= \frac {\sqrt {2 x^{2}-4}\, x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.914 (sec). Leaf size: 48

DSolve[{D[y[x],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*}