Internal problem ID [4372]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 17.
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 (2 x +y\right ) y^{\prime }-x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.049 (sec). Leaf size: 51
dsolve((2*x+y(x))*diff(y(x),x)-(x-2*y(x))=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2 c_{1} x -\sqrt {5 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y \relax (x ) = \frac {-2 c_{1} x +\sqrt {5 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 94
DSolve[(2*x+y[x])*y'[x]-(x-2*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 -\sqrt {5} \sqrt {x^2}-2 x \\ y(x)\to \sqrt {5} \sqrt {x^2}-2 x \\ \end{align*}