31.3.5 problem 5.3

Internal problem ID [5735]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 4
Problem number : 5.3
Date solved : Monday, January 27, 2025 at 01:12:03 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 55

dsolve((x^2+2*x*y(x)-y(x)^2)+(y(x)^2+2*x*y(x)-x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.512 (sec). Leaf size: 75

DSolve[(x^2+2*x*y[x]-y[x]^2)+(y[x]^2+2*x*y[x]-x^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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