Internal problem ID [4479]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {2 x +y+\left (x -2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.042 (sec). Leaf size: 53
dsolve((2*x+y(x))+(x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\frac {c_{1} x}{2}-\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \\ y \relax (x ) = \frac {\frac {c_{1} x}{2}+\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 102
DSolve[(2*x+y[x])+(x-2*y[x])*y'[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*}