Internal problem ID [3199]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 453.
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 {\left (4 x -y\right ) y^{\prime }+2 x -5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
dsolve((4*x-y(x))*diff(y(x),x)+2*x-5*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {4 c_{1} x +\sqrt {-12 c_{1} x +1}-1}{2 c_{1}} \\ y \relax (x ) = \frac {-4 c_{1} x +1+\sqrt {-12 c_{1} x +1}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.957 (sec). Leaf size: 80
DSolve[(4 x-y[x])y'[x]+2 x-5 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-4 x-e^{\frac {c_1}{2}} \sqrt {12 x+e^{c_1}}-e^{c_1}\right ) \\ y(x)\to \frac {1}{2} \left (-4 x+e^{\frac {c_1}{2}} \sqrt {12 x+e^{c_1}}-e^{c_1}\right ) \\ \end{align*}