##### 4.17.28 $$x y(x)^2 y'(x)+y'(x)^2+y(x)^3=0$$

ODE
$x y(x)^2 y'(x)+y'(x)^2+y(x)^3=0$ ODE Classiﬁcation

[[_homogeneous, class G]]

Book solution method
No Missing Variables ODE, Solve for $$x$$

Mathematica
cpu = 0.389853 (sec), leaf count = 57

$\left \{\left \{y(x)\to \frac {\cosh (c_1)-\sinh (c_1)}{-i x+\cosh (c_1)+\sinh (c_1)}\right \},\left \{y(x)\to \frac {\cosh (c_1)-\sinh (c_1)}{i x+\cosh (c_1)+\sinh (c_1)}\right \}\right \}$

Maple
cpu = 0.728 (sec), leaf count = 123

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

DSolve[y[x]^3 + x*y[x]^2*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> (Cosh[C[1]] - Sinh[C[1]])/((-I)*x + Cosh[C[1]] + Sinh[C[1]])}, {y[x] -
> (Cosh[C[1]] - Sinh[C[1]])/(I*x + Cosh[C[1]] + Sinh[C[1]])}}

Maple raw input

dsolve(diff(y(x),x)^2+x*y(x)^2*diff(y(x),x)+y(x)^3 = 0, y(x))

Maple raw output

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