Internal problem ID [3215]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 469.
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 (3+2 x -2 y\right ) y^{\prime }-1-6 x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 36
dsolve((3+2*x-2*y(x))*diff(y(x),x) = 1+6*x-2*y(x),y(x), singsol=all)
\[ y \relax (x ) = 2-\frac {-\left (2 x -1\right ) c_{1}+\sqrt {-2 \left (2 x -1\right )^{2} c_{1}^{2}+1}}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 63
DSolve[(3+2 x-2 y[x])y'[x]==1+6 x-2 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\frac {1}{2} i \sqrt {8 (x-1) x-9-4 c_1}+\frac {3}{2} \\ y(x)\to x+\frac {1}{2} i \sqrt {8 (x-1) x-9-4 c_1}+\frac {3}{2} \\ \end{align*}