25.1.28 problem 28

Internal problem ID [4240]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 28
Date solved : Monday, January 27, 2025 at 08:43:40 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 30

dsolve(x*y(x)*diff(y(x),x)=2*x^2-y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\sqrt {x^{4}+c_{1}}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {x^{4}+c_{1}}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.204 (sec). Leaf size: 38

DSolve[x*y[x]*D[y[x],x]==2*x^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x^4+c_1}}{x} \\ y(x)\to \frac {\sqrt {x^4+c_1}}{x} \\ \end{align*}