ODE
\[ 9 y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _rational]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✓
cpu = 0.406864 (sec), leaf count = 185
\[\left \{\left \{y(x)\to e^{\frac {c_1}{3}} \sqrt [3]{e^{c_1}-i x}\right \},\left \{y(x)\to -\sqrt [3]{-1} e^{\frac {c_1}{3}} \sqrt [3]{e^{c_1}-i x}\right \},\left \{y(x)\to (-1)^{2/3} e^{\frac {c_1}{3}} \sqrt [3]{e^{c_1}-i x}\right \},\left \{y(x)\to e^{\frac {c_1}{3}} \sqrt [3]{i x+e^{c_1}}\right \},\left \{y(x)\to -\sqrt [3]{-1} e^{\frac {c_1}{3}} \sqrt [3]{i x+e^{c_1}}\right \},\left \{y(x)\to (-1)^{2/3} e^{\frac {c_1}{3}} \sqrt [3]{i x+e^{c_1}}\right \}\right \}\]
Maple ✓
cpu = 1.399 (sec), leaf count = 118
\[\left [y \left (x \right ) = \frac {2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{2}, y \left (x \right ) = -\frac {2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, 2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}, y \left (x \right ) = -\frac {2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, 2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}, y \left (x \right ) = \RootOf \left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {-6 \textit {\_a}^{3}+\frac {3 \sqrt {-4 \textit {\_a}^{3}+1}}{2}+\frac {3}{2}}{\textit {\_a} \left (4 \textit {\_a}^{3}-1\right )}d \textit {\_a} +\textit {\_C1} \right ) x^{\frac {2}{3}}\right ]\] Mathematica raw input
DSolve[y[x] - 3*x*y'[x] + 9*y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(C[1]/3)*(E^C[1] - I*x)^(1/3)}, {y[x] -> -((-1)^(1/3)*E^(C[1]/3)*(E^C[1] - I*x)^(1/3))}, {y[x] -> (-1)^(2/3)*E^(C[1]/3)*(E^C[1] - I*x)^(1/3)}, {y[x] -> E^(C[1]/3)*(E^C[1] + I*x)^(1/3)}, {y[x] -> -((-1)^(1/3)*E^(C[1]/3)*(E^C[1] + I*x)^(1/3))}, {y[x] -> (-1)^(2/3)*E^(C[1]/3)*(E^C[1] + I*x)^(1/3)}}
Maple raw input
dsolve(9*y(x)^2*diff(y(x),x)^2-3*x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = 1/2*2^(1/3)*(x^2)^(1/3), y(x) = -1/4*2^(1/3)*(x^2)^(1/3)-1/4*I*3^(1/2)*2^(1/3)*(x^2)^(1/3), y(x) = -1/4*2^(1/3)*(x^2)^(1/3)+1/4*I*3^(1/2)*2^(1/3)*(x^2)^(1/3), y(x) = RootOf(-ln(x)+Intat(3/2*(-4*_a^3+(-4*_a^3+1)^(1/2)+1)/_a/(4*_a^3-1),_a = _Z)+_C1)*x^(2/3)]