Internal problem ID [8549]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 213.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (y+1\right ) y^{\prime }-y=x} \]
✓ Solution by Maple
Time used: 0.5 (sec). Leaf size: 73
dsolve((y(x)+1)*diff(y(x),x)-y(x)-x=0,y(x), singsol=all)
\[ -\frac {\ln \left (-\frac {\left (x -1\right )^{2}-\left (x -1\right ) \left (-y \left (x \right )-1\right )-\left (-y \left (x \right )-1\right )^{2}}{\left (x -1\right )^{2}}\right )}{2}-\frac {\sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (-2 y \left (x \right )-3+x \right ) \sqrt {5}}{5 x -5}\right )}{5}-\ln \left (x -1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 71
DSolve[(y[x]+1)*y'[x]-y[x]-x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {x^2-y(x)^2+(x-3) y(x)-x-1}{(x-1)^2}\right )+\log (1-x)=\frac {\text {arctanh}\left (\frac {y(x)+2 x-1}{\sqrt {5} (y(x)+1)}\right )}{\sqrt {5}}+c_1,y(x)\right ] \]