Internal problem ID [3277]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 533.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 y x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 69
dsolve(x*(4*x-y(x))*diff(y(x),x)+4*x^2-6*x*y(x)-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2 c_{1} x +\frac {1+\sqrt {-12 c_{1}^{2} x^{2}+1}}{2 x c_{1}}}{c_{1}} \\ y \relax (x ) = \frac {-2 c_{1} x -\frac {-1+\sqrt {-12 c_{1}^{2} x^{2}+1}}{2 x c_{1}}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.45 (sec). Leaf size: 90
DSolve[x(4 x -y[x])y'[x]+4 x^2-6 x y[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {4 x^2+e^{\frac {c_1}{2}} \sqrt {12 x^2+e^{c_1}}+e^{c_1}}{2 x} \\ y(x)\to -\frac {4 x^2-e^{\frac {c_1}{2}} \sqrt {12 x^2+e^{c_1}}+e^{c_1}}{2 x} \\ \end{align*}