60.1.128 problem 129

Internal problem ID [10142]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 129
Date solved : Monday, January 27, 2025 at 06:29:48 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

\[ y = \frac {{\mathrm e}^{x}}{-{\mathrm e}^{-1} \left (x +1\right ) \operatorname {Ei}_{1}\left (-x -1\right )-{\mathrm e}^{x}+c_{1} \left (x +1\right )} \]

✓ Solution by Mathematica

Time used: 0.305 (sec). Leaf size: 70

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

\begin{align*} y(x)\to \frac {\exp \left (\int _1^x\frac {K[1]}{K[1]+1}dK[1]\right )}{-\int _1^x-\frac {\exp \left (\int _1^{K[2]}\frac {K[1]}{K[1]+1}dK[1]\right )}{K[2]+1}dK[2]+c_1} \\ y(x)\to 0 \\ \end{align*}