2.48 problem 624

Internal problem ID [8204]

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]]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{\frac {5}{3}}}{y+x^{\frac {4}{3}}}=0} \end {gather*}

Solution by Maple

Time used: 0.972 (sec). Leaf size: 46

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

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

Solution by Mathematica

Time used: 17.141 (sec). Leaf size: 9837

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

Too large to display