64.4.21 problem 22(a)

Internal problem ID [13310]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 22(a)
Date solved : Tuesday, January 28, 2025 at 05:19:23 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.125 (sec). Leaf size: 51

dsolve((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 {5 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y &= \frac {2 c_{1} x +\sqrt {5 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.472 (sec). Leaf size: 94

DSolve[(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 {5 x^2+e^{2 c_1}} \\ y(x)\to 2 x+\sqrt {5 x^2+e^{2 c_1}} \\ y(x)\to 2 x-\sqrt {5} \sqrt {x^2} \\ y(x)\to \sqrt {5} \sqrt {x^2}+2 x \\ \end{align*}