ODE
\[ 2 x y(x)^3 y'(x)+y'(x)^2+y(x)^4=0 \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 0.773611 (sec), leaf count = 199
\[\left \{\text {Solve}\left [\frac {\sqrt {x^2 y(x)^2-1} y(x)^2 \left (c_1+\log (y(x))\right )+\sqrt {y(x)^4 \left (x^2 y(x)^2-1\right )} \left (\log (y(x))-\log \left (y(x) \left (\sqrt {x^2 y(x)^2-1}+x y(x)\right )\right )\right )}{y(x) \sqrt {x^2 y(x)^2-1}}=0,y(x)\right ],\text {Solve}\left [\frac {\sqrt {x^2 y(x)^2-1} y(x)^2 \left (c_1+\log (y(x))\right )+\sqrt {y(x)^4 \left (x^2 y(x)^2-1\right )} \left (\log \left (y(x) \left (\sqrt {x^2 y(x)^2-1}+x y(x)\right )\right )-\log (y(x))\right )}{y(x) \sqrt {x^2 y(x)^2-1}}=0,y(x)\right ]\right \}\]
Maple ✓
cpu = 0.075 (sec), leaf count = 81
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-{x}^{-2}=0,\ln \left ( x \right ) -{\it \_C1}-\ln \left ( xy \left ( x \right ) +\sqrt {{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) -\ln \left ( xy \left ( x \right ) \right ) =0,\ln \left ( x \right ) -{\it \_C1}+\ln \left ( xy \left ( x \right ) +\sqrt {{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) -\ln \left ( xy \left ( x \right ) \right ) =0 \right \} \] Mathematica raw input
DSolve[y[x]^4 + 2*x*y[x]^3*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{Solve[((C[1] + Log[y[x]])*y[x]^2*Sqrt[-1 + x^2*y[x]^2] + (Log[y[x]] - Log[y[x]*(x*y[x] + Sqrt[-1 + x^2*y[x]^2])])*Sqrt[y[x]^4*(-1 + x^2*y[x]^2)])/(y[x]*Sqrt[-1 + x^2*y[x]^2]) == 0, y[x]], Solve[((C[1] + Log[y[x]])*y[x]^2*Sqrt[-1 + x^2*y[x]^2] + (-Log[y[x]] + Log[y[x]*(x*y[x] + Sqrt[-1 + x^2*y[x]^2])])*Sqrt[y[x]^4*(-1 + x^2*y[x]^2)])/(y[x]*Sqrt[-1 + x^2*y[x]^2]) == 0, y[x]]}
Maple raw input
dsolve(diff(y(x),x)^2+2*x*y(x)^3*diff(y(x),x)+y(x)^4 = 0, y(x),'implicit')
Maple raw output
y(x)^2-1/x^2 = 0, ln(x)-_C1+ln(x*y(x)+(x^2*y(x)^2-1)^(1/2))-ln(x*y(x)) = 0, ln(x)-_C1-ln(x*y(x)+(x^2*y(x)^2-1)^(1/2))-ln(x*y(x)) = 0