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 = 0.485601 (sec), leaf count = 231
\[\left \{\left \{y(x)\to -e^{\frac {c_1}{4}} \sqrt [4]{e^{c_1}-2 i x}\right \},\left \{y(x)\to -i e^{\frac {c_1}{4}} \sqrt [4]{e^{c_1}-2 i x}\right \},\left \{y(x)\to i e^{\frac {c_1}{4}} \sqrt [4]{e^{c_1}-2 i x}\right \},\left \{y(x)\to e^{\frac {c_1}{4}} \sqrt [4]{e^{c_1}-2 i x}\right \},\left \{y(x)\to -e^{\frac {c_1}{4}} \sqrt [4]{2 i x+e^{c_1}}\right \},\left \{y(x)\to -i e^{\frac {c_1}{4}} \sqrt [4]{2 i x+e^{c_1}}\right \},\left \{y(x)\to i e^{\frac {c_1}{4}} \sqrt [4]{2 i x+e^{c_1}}\right \},\left \{y(x)\to e^{\frac {c_1}{4}} \sqrt [4]{2 i x+e^{c_1}}\right \}\right \}\]
Maple ✓
cpu = 1.386 (sec), leaf count = 79
\[\left [y \left (x \right ) = \sqrt {x}, y \left (x \right ) = \sqrt {-x}, y \left (x \right ) = -\sqrt {x}, y \left (x \right ) = -\sqrt {-x}, y \left (x \right ) = \RootOf \left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {-2 \textit {\_a}^{4}+2 \sqrt {-\textit {\_a}^{4}+1}+2}{\textit {\_a} \left (\textit {\_a}^{4}-1\right )}d \textit {\_a} +\textit {\_C1} \right ) \sqrt {x}\right ]\] 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]/4)*(E^C[1] - (2*I)*x)^(1/4))}, {y[x] -> (-I)*E^(C[1]/4)*(E^C[1] - (2*I)*x)^(1/4)}, {y[x] -> I*E^(C[1]/4)*(E^C[1] - (2*I)*x)^(1/4)}, {y[x] -> E^(C[1]/4)*(E^C[1] - (2*I)*x)^(1/4)}, {y[x] -> -(E^(C[1]/4)*(E^C[1] + (2*I)*x)^(1/4))}, {y[x] -> (-I)*E^(C[1]/4)*(E^C[1] + (2*I)*x)^(1/4)}, {y[x] -> I*E^(C[1]/4)*(E^C[1] + (2*I)*x)^(1/4)}, {y[x] -> E^(C[1]/4)*(E^C[1] + (2*I)*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))
Maple raw output
[y(x) = x^(1/2), y(x) = (-x)^(1/2), y(x) = -x^(1/2), y(x) = -(-x)^(1/2), y(x) = RootOf(-ln(x)+Intat(2*(-_a^4+(-_a^4+1)^(1/2)+1)/_a/(_a^4-1),_a = _Z)+_C1)*x^(1/2)]