4.9.12 \(X^{2/3} y'(x)=Y^{2/3}\)

ODE
\[ X^{2/3} y'(x)=Y^{2/3} \] ODE Classification

[_quadrature]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00294672 (sec), leaf count = 20

\[\left \{\left \{y(x)\to c_1+\frac {x Y^{2/3}}{X^{2/3}}\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 14

\[ \left \{ y \relax (x ) ={x{Y}^{{\frac {2}{3}}}{X}^{-{\frac {2}{3}}}}+{\it \_C1} \right \} \] Mathematica raw input

DSolve[X^(2/3)*y'[x] == Y^(2/3),y[x],x]

Mathematica raw output

{{y[x] -> (x*Y^(2/3))/X^(2/3) + C[1]}}

Maple raw input

dsolve(X^(2/3)*diff(y(x),x) = Y^(2/3), y(x),'implicit')

Maple raw output

y(x) = Y^(2/3)/X^(2/3)*x+_C1