Internal problem ID [8959]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 624.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]]
\[ \boxed {y^{\prime }-\frac {x^{\frac {5}{3}}}{y+x^{\frac {4}{3}}}=0} \]
✓ Solution by Maple
Time used: 0.579 (sec). Leaf size: 46
dsolve(diff(y(x),x) = x^(5/3)/(y(x)+x^(4/3)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{192}+12 x^{\frac {4}{3}} \textit {\_Z}^{176}+48 x^{\frac {8}{3}} \textit {\_Z}^{160}+64 x^{4} \textit {\_Z}^{144}-c_{1} \right )^{16}}{2}+\frac {x^{\frac {4}{3}}}{2} \]
✓ Solution by Mathematica
Time used: 79.305 (sec). Leaf size: 9837
DSolve[y'[x] == x^(5/3)/(x^(4/3) + y[x]),y[x],x,IncludeSingularSolutions -> True]
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