60.2.268 problem 844
Internal
problem
ID
[10855]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
844
Date
solved
:
Monday, January 27, 2025 at 10:15:36 PM
CAS
classification
:
[_rational, [_Abel, `2nd type`, `class C`]]
\begin{align*} y^{\prime }&=\frac {y \left (x +y\right ) \left (y+1\right )}{x \left (y x +x +y\right )} \end{align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 106
dsolve(diff(y(x),x) = y(x)*(x+y(x))*(y(x)+1)/x/(x*y(x)+x+y(x)),y(x), singsol=all)
\[
y = -\frac {{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left ({\mathrm e}^{\textit {\_Z}}+9\right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}+9\right )} x}{{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left ({\mathrm e}^{\textit {\_Z}}+9\right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}+9\right )} x +{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left ({\mathrm e}^{\textit {\_Z}}+9\right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}+9\right )}+9}
\]
✓ Solution by Mathematica
Time used: 1.377 (sec). Leaf size: 105
DSolve[D[y[x],x] == (y[x]*(1 + y[x])*(x + y[x]))/(x*(x + y[x] + x*y[x])),y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\int _1^{\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 (x+(x-2) y(x))}{\sqrt [3]{2} x^4 (x+(x+1) y(x))}}\frac {1}{K[1]^3-\frac {3 K[1]}{2^{2/3}}+1}dK[1]=\frac {2^{2/3} \left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2}{9 x^3}+c_1,y(x)\right ]
\]