Internal problem ID [3210]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 464.
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 {\left (x -2 y\right ) y^{\prime }+2 x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 53
dsolve((x-2*y(x))*diff(y(x),x)+2*x+y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\frac {c_{1} x}{2}-\frac {\sqrt {5 x^{2} c_{1}^{2}+4}}{2}}{c_{1}} \\ y \relax (x ) = \frac {\frac {c_{1} x}{2}+\frac {\sqrt {5 x^{2} c_{1}^{2}+4}}{2}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.479 (sec). Leaf size: 102
DSolve[(x-2 y[x])y'[x]+2 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*}