ODE
\[ \left (x^3-y(x)^4\right ) y'(x)=3 x^2 y(x) \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.402734 (sec), leaf count = 1021
\[\left \{\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}+\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}}-\frac {1}{2} \sqrt {-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}-\frac {6 c_1}{\sqrt {\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}+\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}}}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}+\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}}+\frac {1}{2} \sqrt {-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}-\frac {6 c_1}{\sqrt {\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}+\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}}}}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}+\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}}-\frac {1}{2} \sqrt {-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}+\frac {6 c_1}{\sqrt {\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}+\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}}}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}+\frac {6 c_1}{\sqrt {\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}+\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}}}}-\frac {1}{2} \sqrt {\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}+\frac {\sqrt [3]{9 c_1{}^2-\sqrt {81 c_1{}^4-256 x^9}}}{\sqrt [3]{2}}}\right \}\right \}\]
Maple ✓
cpu = 0.431 (sec), leaf count = 25
\[\left [y \left (x \right ) = \RootOf \left (x^{9} \textit {\_Z}^{4}+3-{\mathrm e}^{\frac {9 \textit {\_C1}}{4}} \textit {\_Z} \right ) x^{3}\right ]\] Mathematica raw input
DSolve[(x^3 - y[x]^4)*y'[x] == 3*x^2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[(4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) + (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3)]/2 - Sqrt[(-4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) - (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3) - (6*C[1])/Sqrt[(4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) + (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3)]]/2}, {y[x] -> Sqrt[(4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) + (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3)]/2 + Sqrt[(-4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) - (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3) - (6*C[1])/Sqrt[(4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) + (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3)]]/2}, {y[x] -> -1/2*Sqrt[(4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) + (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3)] - Sqrt[(-4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) - (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3) + (6*C[1])/Sqrt[(4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) + (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3)]]/2}, {y[x] -> -1/2*Sqrt[(4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) + (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3)] + Sqrt[(-4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) - (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3) + (6*C[1])/Sqrt[(4*2^(1/3)*x^3)/(9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3) + (9*C[1]^2 - Sqrt[-256*x^9 + 81*C[1]^4])^(1/3)/2^(1/3)]]/2}}
Maple raw input
dsolve((x^3-y(x)^4)*diff(y(x),x) = 3*x^2*y(x), y(x))
Maple raw output
[y(x) = RootOf(x^9*_Z^4+3-exp(9/4*_C1)*_Z)*x^3]