ODE
\[ 4 y(x)^3 y'(x)^2-4 x y'(x)+y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _rational]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 0.15202 (sec), leaf count = 99
\[\left \{\left \{y(x)\to -\sqrt [4]{-e^{c_1} \left (e^{c_1}-2 x\right )}\right \},\left \{y(x)\to -i \sqrt [4]{-e^{c_1} \left (e^{c_1}-2 x\right )}\right \},\left \{y(x)\to i \sqrt [4]{-e^{c_1} \left (e^{c_1}-2 x\right )}\right \},\left \{y(x)\to \sqrt [4]{-e^{c_1} \left (e^{c_1}-2 x\right )}\right \}\right \}\]
Maple ✓
cpu = 1.243 (sec), leaf count = 60
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{4}-{x}^{2}=0,\ln \left ( x \right ) -\int ^{{y \left ( x \right ) {\frac {1}{\sqrt {x}}}}}\!{\frac {1}{{{\it \_a}}^{5}-{\it \_a}} \left ( -2\,{{\it \_a}}^{4}+2\,\sqrt {-{{\it \_a}}^{4}+1}+2 \right ) }{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y[x] - 4*x*y'[x] + 4*y[x]^3*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(-(E^C[1]*(E^C[1] - 2*x)))^(1/4)}, {y[x] -> (-I)*(-(E^C[1]*(E^C[1] - 2*x)))^(1/4)}, {y[x] -> I*(-(E^C[1]*(E^C[1] - 2*x)))^(1/4)}, {y[x] -> (-(E^C[1]*(E^C[1] - 2*x)))^(1/4)}}
Maple raw input
dsolve(4*y(x)^3*diff(y(x),x)^2-4*x*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x)^4-x^2 = 0, ln(x)-Intat((-2*_a^4+2*(-_a^4+1)^(1/2)+2)/(_a^5-_a),_a = y(x)/x^(1/2))-_C1 = 0