64.3.1 problem 1

Internal problem ID [13272]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 05:13:49 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x +2 y+\left (2 x +y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.118 (sec). Leaf size: 49

dsolve((3*x+2*y(x))+(2*x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.555 (sec). Leaf size: 79

DSolve[(3*x+2*y[x])+(2*x+y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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