36.3.10 problem 10

Internal problem ID [6331]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 10
Date solved : Monday, January 27, 2025 at 01:56:42 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {c_1 x -\sqrt {5 x^{2} c_1^{2}+4}}{2 c_1} \\ y &= \frac {c_1 x +\sqrt {5 x^{2} c_1^{2}+4}}{2 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.456 (sec). Leaf size: 102

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

\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x+\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x-\sqrt {5} \sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}+x\right ) \\ \end{align*}