60.2.48 problem 624

Internal problem ID [10635]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 624
Date solved : Monday, January 27, 2025 at 09:19:07 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \end{align*}

✓ Solution by Maple

Time used: 0.843 (sec). Leaf size: 46

dsolve(diff(y(x),x) = x^(5/3)/(y(x)+x^(4/3)),y(x), singsol=all)
 

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{192}+12 x^{{4}/{3}} \textit {\_Z}^{176}+48 x^{{8}/{3}} \textit {\_Z}^{160}+64 x^{4} \textit {\_Z}^{144}-c_{1} \right )^{16}}{2}+\frac {x^{{4}/{3}}}{2} \]

✓ Solution by Mathematica

Time used: 76.140 (sec). Leaf size: 9837

DSolve[D[y[x],x] == x^(5/3)/(x^(4/3) + y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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