60.2.222 problem 798

Internal problem ID [10809]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 798
Date solved : Tuesday, January 28, 2025 at 05:16:37 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {\left (x +y+1\right ) y}{\left (2 y^{3}+y+x \right ) \left (1+x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 30

dsolve(diff(y(x),x) = 1/(2*y(x)^3+y(x)+x)*(x+y(x)+1)*y(x)/(x+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.394 (sec). Leaf size: 65

DSolve[D[y[x],x] == (y[x]*(1 + x + y[x]))/((1 + x)*(x + y[x] + 2*y[x]^3)),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x\left (-\frac {1}{y(x)}-\frac {1}{K[1]+1}\right )dK[1]+\int _1^{y(x)}\left (\frac {x}{K[2]^2}+2 K[2]-\int _1^x\frac {1}{K[2]^2}dK[1]+\frac {1}{K[2]}\right )dK[2]=c_1,y(x)\right ] \]