Internal problem ID [7794]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 214.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (y+x -1\right ) y^{\prime }-y+2 x +3=0} \end {gather*}
✓ Solution by Maple
Time used: 0.719 (sec). Leaf size: 56
dsolve((y(x)+x-1)*diff(y(x),x)-y(x)+2*x+3=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {5}{3}-\frac {\tan \left (\RootOf \left (\sqrt {2}\, \ln \left (2 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) \left (3 x +2\right )^{2}+2 \left (3 x +2\right )^{2}\right )+2 \sqrt {2}\, c_{1}-2 \textit {\_Z} \right )\right ) \left (3 x +2\right ) \sqrt {2}}{3} \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 78
DSolve[(y[x]+x-1)*y'[x]-y[x]+2*x+3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \sqrt {2} \text {ArcTan}\left (\frac {-y(x)+2 x+3}{\sqrt {2} (y(x)+x-1)}\right )=2 \log \left (\frac {6 x^2+3 y(x)^2-10 y(x)+8 x+11}{(3 x+2)^2}\right )+4 \log (3 x+2)+3 c_1,y(x)\right ] \]