Internal problem ID [8550]
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`]]
\[ \boxed {\left (x +y-1\right ) y^{\prime }-y=-2 x -3} \]
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 51
dsolve((y(x)+x-1)*diff(y(x),x)-y(x)+2*x+3=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {5}{3}+\frac {\tan \left (\operatorname {RootOf}\left (\sqrt {2}\, \ln \left (2\right )+\sqrt {2}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (3 x +2\right )^{2}\right )+2 c_{1} \sqrt {2}-2 \textit {\_Z} \right )\right ) \sqrt {2}\, \left (-3 x -2\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 78
DSolve[(y[x]+x-1)*y'[x]-y[x]+2*x+3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \sqrt {2} \arctan \left (\frac {-y(x)+2 x+3}{\sqrt {2} (y(x)+x-1)}\right )=2 \log \left (\frac {6 x^2+3 y(x)^2-10 y(x)+8 x+11}{(3 x+2)^2}\right )+4 \log (3 x+2)+3 c_1,y(x)\right ] \]