Internal problem ID [3211]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 465.
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 (1+x -2 y\right ) y^{\prime }-1-2 x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 38
dsolve((1+x-2*y(x))*diff(y(x),x) = 1+2*x-y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{3}-\frac {-\frac {\left (1+3 x \right ) c_{1}}{2}+\frac {\sqrt {-3 \left (1+3 x \right )^{2} c_{1}^{2}+4}}{2}}{3 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.107 (sec). Leaf size: 65
DSolve[(1+x-2 y[x])y'[x]==1+2 x-y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x-i \sqrt {x (3 x+2)-1-4 c_1}+1\right ) \\ y(x)\to \frac {1}{2} \left (x+i \sqrt {x (3 x+2)-1-4 c_1}+1\right ) \\ \end{align*}