Internal problem ID [110]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 32.
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 {4 x -y+\left (-x +6 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 53
dsolve(4*x-y(x)+(-x+6*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\frac {x c_{1}}{6}-\frac {\sqrt {-23 c_{1}^{2} x^{2}+12}}{6}}{c_{1}} \\ y \relax (x ) = \frac {\frac {x c_{1}}{6}+\frac {\sqrt {-23 c_{1}^{2} x^{2}+12}}{6}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.157 (sec). Leaf size: 106
DSolve[4*x-y[x]+(-x+6*y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (x-\sqrt {-23 x^2+12 e^{c_1}}\right ) \\ y(x)\to \frac {1}{6} \left (x+\sqrt {-23 x^2+12 e^{c_1}}\right ) \\ y(x)\to \frac {1}{6} \left (x-\sqrt {23} \sqrt {-x^2}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt {23} \sqrt {-x^2}+x\right ) \\ \end{align*}