4.19.38 \(x^4 y'(x)^2+2 x^3 y(x) y'(x)-4=0\)

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 = 0.630521 (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 = 0.07 (sec), leaf count = 43

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+4\,{x}^{-2}=0,\ln \relax (x ) -{\it \_C1}-{\it Arcsinh} \left ({\frac {xy \relax (x ) }{2}} \right ) =0,\ln \relax (x ) -{\it \_C1}+{\it Arcsinh} \left ({\frac {xy \relax (x ) }{2}} \right ) =0 \right \} \] 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),'implicit')

Maple raw output

y(x)^2+4/x^2 = 0, ln(x)-_C1+arcsinh(1/2*x*y(x)) = 0, ln(x)-_C1-arcsinh(1/2*x*y(x
)) = 0