60.2.247 problem 823

Internal problem ID [10834]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 823
Date solved : Monday, January 27, 2025 at 10:11:17 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x +y+y^{3}+y^{4}\right )} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 38

dsolve(diff(y(x),x) = y(x)*(x+y(x))/x/(x+y(x)+y(x)^3+y(x)^4),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-2 \,{\mathrm e}^{4 \textit {\_Z}}-3 \,{\mathrm e}^{3 \textit {\_Z}}+6 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+6 c_{1} {\mathrm e}^{\textit {\_Z}}-6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+6 x \right )} \]

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 41

DSolve[D[y[x],x] == (y[x]*(x + y[x]))/(x*(x + y[x] + y[x]^3 + y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
 

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