82.12.28 problem Ex. 30

Internal problem ID [18793]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 30
Date solved : Tuesday, January 28, 2025 at 12:17:39 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 47

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

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

✓ Solution by Mathematica

Time used: 0.984 (sec). Leaf size: 66

DSolve[2*x*y[x]+(y[x]^2-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+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*}