Internal problem ID [3719]
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`]]
\[ \boxed {\left (1+x -2 y\right ) y^{\prime }+y=1+2 x} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 38
dsolve((1+x-2*y(x))*diff(y(x),x) = 1+2*x-y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{3}-\frac {-\frac {\left (3 x +1\right ) c_{1}}{2}+\frac {\sqrt {-3 \left (3 x +1\right )^{2} c_{1}^{2}+4}}{2}}{3 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 67
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 (-i \sqrt {3 x^2+2 x-1-4 c_1}+x+1\right ) y(x)\to \frac {1}{2} \left (i \sqrt {3 x^2+2 x-1-4 c_1}+x+1\right ) \end{align*}