7.5.11 problem 11

Internal problem ID [115]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 11
Date solved : Friday, February 07, 2025 at 07:51:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.040 (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 &= \frac {1-\sqrt {-4 c_1^{2} x^{2}+1}}{2 c_1} \\ y &= \frac {1+\sqrt {-4 c_1^{2} x^{2}+1}}{2 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.082 (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*}