Internal problem ID [1903]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x -y}{x +4 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 53
dsolve(diff(y(x),x)=(2*x-y(x))/(x+4*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-\frac {x c_{1}}{4}-\frac {\sqrt {9 x^{2} c_{1}^{2}+8}}{4}}{c_{1}} \\ y \relax (x ) = \frac {-\frac {x c_{1}}{4}+\frac {\sqrt {9 x^{2} c_{1}^{2}+8}}{4}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.492 (sec). Leaf size: 101
DSolve[y'[x]==(2*x-y[x])/(x+4*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-x-\sqrt {9 x^2+8 e^{c_1}}\right ) \\ y(x)\to \frac {1}{4} \left (-x+\sqrt {9 x^2+8 e^{c_1}}\right ) \\ y(x)\to \frac {1}{4} \left (-3 \sqrt {x^2}-x\right ) \\ y(x)\to \frac {1}{4} \left (3 \sqrt {x^2}-x\right ) \\ \end{align*}