32.6.9 problem Exercise 12.9, page 103

Internal problem ID [5874]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.9, page 103
Date solved : Monday, January 27, 2025 at 01:22:46 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 47

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

\begin{align*} y \left (x \right ) &= \frac {1-\sqrt {-4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ y \left (x \right ) &= \frac {1+\sqrt {-4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.149 (sec). Leaf size: 66

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

\begin{align*} y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {-4 x^2+e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {-4 x^2+e^{2 c_1}}+e^{c_1}\right ) \\ y(x)\to 0 \\ \end{align*}