Internal problem ID [1903]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 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`]]
\[ \boxed {y^{\prime }-\frac {2 x -y}{x +4 y}=0} \]
✓ 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 \left (x \right ) &= \frac {-c_{1} x -\sqrt {9 c_{1}^{2} x^{2}+8}}{4 c_{1}} \\ y \left (x \right ) &= \frac {-c_{1} x +\sqrt {9 c_{1}^{2} x^{2}+8}}{4 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.472 (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*}