Internal problem ID [8412]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 832.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (x +y+1\right ) y}{\left (y^{4}+y^{3}+y^{2}+x \right ) \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x) = 1/(y(x)^4+y(x)^3+y(x)^2+x)*(x+y(x)+1)*y(x)/(x+1),y(x), singsol=all)
\[ \ln \left (x +1\right )+\frac {x}{y \relax (x )}-\frac {y \relax (x )^{3}}{3}-\frac {y \relax (x )^{2}}{2}-y \relax (x )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 61.234 (sec). Leaf size: 2405
DSolve[y'[x] == (y[x]*(1 + x + y[x]))/((1 + x)*(x + y[x]^2 + y[x]^3 + y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
Too large to display