ODE
\[ x^4 y'(x)^2+2 x^3 y(x) y'(x)-4=0 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 0.623791 (sec), leaf count = 49
\[\left \{\left \{y(x)\to \frac {e^{c_1}}{2 x^2}-2 e^{-c_1}\right \},\left \{y(x)\to \frac {e^{-c_1}}{2}-\frac {2 e^{c_1}}{x^2}\right \}\right \}\]
Maple ✓
cpu = 0.233 (sec), leaf count = 49
\[\left [y \left (x \right ) = -\frac {2 i}{x}, y \left (x \right ) = \frac {2 i}{x}, y \left (x \right ) = \frac {2 \sinh \left (-\ln \left (x \right )+\textit {\_C1} \right )}{x}, y \left (x \right ) = -\frac {2 \sinh \left (-\ln \left (x \right )+\textit {\_C1} \right )}{x}\right ]\] Mathematica raw input
DSolve[-4 + 2*x^3*y[x]*y'[x] + x^4*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -2/E^C[1] + E^C[1]/(2*x^2)}, {y[x] -> 1/(2*E^C[1]) - (2*E^C[1])/x^2}}
Maple raw input
dsolve(x^4*diff(y(x),x)^2+2*x^3*y(x)*diff(y(x),x)-4 = 0, y(x))
Maple raw output
[y(x) = -2*I/x, y(x) = 2*I/x, y(x) = 2*sinh(-ln(x)+_C1)/x, y(x) = -2*sinh(-ln(x)+_C1)/x]