82.3.2 problem Ex. 2

Internal problem ID [18732]
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. Exercises at page 16
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:13:11 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 2.369 (sec). Leaf size: 80

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

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