Internal problem ID [11634]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y+\left (2 x -y\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) &= \frac {2 c_{1} x -\sqrt {5 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y \left (x \right ) &= \frac {2 c_{1} x +\sqrt {5 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.777 (sec). Leaf size: 94
DSolve[(x+2*y[x])+(2*x-y[x])*y'[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*}