8.5.11 problem 11

Internal problem ID [739]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 11
Date solved : Wednesday, February 05, 2025 at 03:57:04 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: 0.014 (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: 0.914 (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*}