ODE
\[ 4 y(x) y'(x)+4 x y'(x)^2-y(x)^4=0 \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 0.194342 (sec), leaf count = 123
\[\left \{\left \{y(x)\to -\frac {\sqrt {\tanh ^2\left (\frac {1}{2} \left (c_1-\log (x)\right )\right )-1}}{\sqrt {x}}\right \},\left \{y(x)\to \frac {\sqrt {\tanh ^2\left (\frac {1}{2} \left (c_1-\log (x)\right )\right )-1}}{\sqrt {x}}\right \},\left \{y(x)\to -\frac {\sqrt {\tanh ^2\left (\frac {1}{2} \left (\log (x)-c_1\right )\right )-1}}{\sqrt {x}}\right \},\left \{y(x)\to \frac {\sqrt {\tanh ^2\left (\frac {1}{2} \left (\log (x)-c_1\right )\right )-1}}{\sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 53
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}+{x}^{-1}=0,\ln \left ( x \right ) -{\it \_C1}-2\,{\it Artanh} \left ( {\frac {1}{\sqrt {1+x \left ( y \left ( x \right ) \right ) ^{2}}}} \right ) =0,\ln \left ( x \right ) -{\it \_C1}+2\,{\it Artanh} \left ( {\frac {1}{\sqrt {1+x \left ( y \left ( x \right ) \right ) ^{2}}}} \right ) =0 \right \} \] Mathematica raw input
DSolve[-y[x]^4 + 4*y[x]*y'[x] + 4*x*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[-1 + Tanh[(C[1] - Log[x])/2]^2]/Sqrt[x])}, {y[x] -> Sqrt[-1 + Tanh[(C[1] - Log[x])/2]^2]/Sqrt[x]}, {y[x] -> -(Sqrt[-1 + Tanh[(-C[1] + Log[x])/2]^2]/Sqrt[x])}, {y[x] -> Sqrt[-1 + Tanh[(-C[1] + Log[x])/2]^2]/Sqrt[x]}}
Maple raw input
dsolve(4*x*diff(y(x),x)^2+4*y(x)*diff(y(x),x)-y(x)^4 = 0, y(x),'implicit')
Maple raw output
y(x)^2+1/x = 0, ln(x)-_C1+2*arctanh(1/(1+x*y(x)^2)^(1/2)) = 0, ln(x)-_C1-2*arctanh(1/(1+x*y(x)^2)^(1/2)) = 0