Internal problem ID [3231]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 485.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (5+2 x -4 y\right ) y^{\prime }-3-x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 41
dsolve((5+2*x-4*y(x))*diff(y(x),x) = 3+x-2*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x}{2}+\frac {5}{4}-\frac {\sqrt {4 c_{1}-4 x +25}}{4} \\ y \relax (x ) = \frac {x}{2}+\frac {5}{4}+\frac {\sqrt {4 c_{1}-4 x +25}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 61
DSolve[(5+2 x-4 y[x])y'[x]==3+x-2 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (2 x-i \sqrt {4 x-25-16 c_1}+5\right ) \\ y(x)\to \frac {1}{4} \left (2 x+i \sqrt {4 x-25-16 c_1}+5\right ) \\ \end{align*}