15.8.2 problem 2

Internal problem ID [3005]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:07:26 AM
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: 0.083 (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 &= \frac {1+\sqrt {c_{1} x^{2}+1}}{c_{1} x} \\ y &= \frac {1-\sqrt {c_{1} x^{2}+1}}{c_{1} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.457 (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*}