4.21.43 \(-x y(x)^4 y'(x)+y'(x)^3-y(x)^5=0\)

ODE
\[ -x y(x)^4 y'(x)+y'(x)^3-y(x)^5=0 \] ODE Classification

[[_1st_order, _with_linear_symmetries]]

Book solution method
No Missing Variables ODE, Solve for \(x\)

Mathematica ✓
cpu = 0.17863 (sec), leaf count = 18

\[\left \{\left \{y(x)\to \frac {1}{c_1 x-c_1{}^3}\right \}\right \}\]

Maple ✓
cpu = 1.795 (sec), leaf count = 43

\[\left [y \left (x \right ) = -\frac {3 \sqrt {3}}{2 x^{\frac {3}{2}}}, y \left (x \right ) = \frac {3 \sqrt {3}}{2 x^{\frac {3}{2}}}, y \left (x \right ) = \textit {\_C1} \sqrt {\frac {\textit {\_C1}^{10}}{\left (\textit {\_C1}^{4} x -1\right )^{2}}}\right ]\] Mathematica raw input

DSolve[-y[x]^5 - x*y[x]^4*y'[x] + y'[x]^3 == 0,y[x],x]

Mathematica raw output

{{y[x] -> (x*C[1] - C[1]^3)^(-1)}}

Maple raw input

dsolve(diff(y(x),x)^3-x*y(x)^4*diff(y(x),x)-y(x)^5 = 0, y(x))

Maple raw output

[y(x) = -3/2*3^(1/2)/x^(3/2), y(x) = 3/2*3^(1/2)/x^(3/2), y(x) = _C1*(_C1^10/(_C
1^4*x-1)^2)^(1/2)]