60.1.212 problem 213

Internal problem ID [10226]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 213
Date solved : Monday, January 27, 2025 at 06:40:08 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y+1\right ) y^{\prime }-y-x&=0 \end{align*}

✓ Solution by Maple

Time used: 3.810 (sec). Leaf size: 66

dsolve((y(x)+1)*diff(y(x),x)-y(x)-x=0,y(x), singsol=all)
 

\[ -\frac {\ln \left (\frac {y^{2}+\left (-x +3\right ) y-x^{2}+x +1}{\left (x -1\right )^{2}}\right )}{2}-\frac {\sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (-2 y-3+x \right ) \sqrt {5}}{5 x -5}\right )}{5}-\ln \left (x -1\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 71

DSolve[(y[x]+1)*D[y[x],x]-y[x]-x==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {x^2-y(x)^2+(x-3) y(x)-x-1}{(x-1)^2}\right )+\log (1-x)=\frac {\text {arctanh}\left (\frac {y(x)+2 x-1}{\sqrt {5} (y(x)+1)}\right )}{\sqrt {5}}+c_1,y(x)\right ] \]