ODE
\[ y'(x)^4+4 y(x) y'(x)^3+6 y(x)^2 y'(x)^2-\left (1-4 y(x)^3\right ) y'(x)-y(x) \left (3-y(x)^3\right )=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Use new variable
Mathematica ✓
cpu = 153.708 (sec), leaf count = 2925
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{-12 K[1]+6^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[1]^3+27}+9} K[1]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[1]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[1]^3+27}+9\right )^{2/3}}}-6 \sqrt [6]{2} \sqrt [12]{3} \sqrt {-\frac {1024\ 2^{2/3} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[1]^3+27}+9} K[1]^3+128 \sqrt [3]{3} \sqrt {2048 K[1]^3+27} K[1]^2+384\ 3^{5/6} K[1]^2-16 \sqrt [3]{2} \sqrt {2048 K[1]^3+27} \left (\sqrt {3} \sqrt {2048 K[1]^3+27}+9\right )^{2/3} K[1]-48 \sqrt [3]{2} \sqrt {3} \left (\sqrt {3} \sqrt {2048 K[1]^3+27}+9\right )^{2/3} K[1]-2\ 3^{2/3} \sqrt {2048 K[1]^3+27} \left (\sqrt {3} \sqrt {2048 K[1]^3+27}+9\right )^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[1]^3+27}+9} K[1]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[1]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[1]^3+27}+9\right )^{2/3}}}-18 \sqrt [6]{3} \left (\sqrt {3} \sqrt {2048 K[1]^3+27}+9\right )^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[1]^3+27}+9} K[1]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[1]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[1]^3+27}+9\right )^{2/3}}}+3\ 6^{2/3} \sqrt {2048 K[1]^3+27} \sqrt [3]{\sqrt {3} \sqrt {2048 K[1]^3+27}+9}+27\ 2^{2/3} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[1]^3+27}+9}}{\left (\sqrt {3} \sqrt {2048 K[1]^3+27}+9\right ) \left (-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[1]^3+27}+9} K[1]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[1]^3+27}+9 \sqrt [3]{2}\right )}}}dK[1]\& \right ]\left [\frac {x}{12}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{-12 K[2]+6^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[2]^3+27}+9} K[2]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[2]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[2]^3+27}+9\right )^{2/3}}}+6 \sqrt [6]{2} \sqrt [12]{3} \sqrt {-\frac {1024\ 2^{2/3} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[2]^3+27}+9} K[2]^3+128 \sqrt [3]{3} \sqrt {2048 K[2]^3+27} K[2]^2+384\ 3^{5/6} K[2]^2-16 \sqrt [3]{2} \sqrt {2048 K[2]^3+27} \left (\sqrt {3} \sqrt {2048 K[2]^3+27}+9\right )^{2/3} K[2]-48 \sqrt [3]{2} \sqrt {3} \left (\sqrt {3} \sqrt {2048 K[2]^3+27}+9\right )^{2/3} K[2]-2\ 3^{2/3} \sqrt {2048 K[2]^3+27} \left (\sqrt {3} \sqrt {2048 K[2]^3+27}+9\right )^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[2]^3+27}+9} K[2]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[2]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[2]^3+27}+9\right )^{2/3}}}-18 \sqrt [6]{3} \left (\sqrt {3} \sqrt {2048 K[2]^3+27}+9\right )^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[2]^3+27}+9} K[2]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[2]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[2]^3+27}+9\right )^{2/3}}}+3\ 6^{2/3} \sqrt {2048 K[2]^3+27} \sqrt [3]{\sqrt {3} \sqrt {2048 K[2]^3+27}+9}+27\ 2^{2/3} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[2]^3+27}+9}}{\left (\sqrt {3} \sqrt {2048 K[2]^3+27}+9\right ) \left (-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[2]^3+27}+9} K[2]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[2]^3+27}+9 \sqrt [3]{2}\right )}}}dK[2]\& \right ]\left [\frac {x}{12}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{12 K[3]+6^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[3]^3+27}+9} K[3]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[3]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[3]^3+27}+9\right )^{2/3}}}+6 \sqrt [6]{2} \sqrt [12]{3} \sqrt {-\frac {1024\ 2^{2/3} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[3]^3+27}+9} K[3]^3+128 \sqrt [3]{3} \sqrt {2048 K[3]^3+27} K[3]^2+384\ 3^{5/6} K[3]^2-16 \sqrt [3]{2} \sqrt {2048 K[3]^3+27} \left (\sqrt {3} \sqrt {2048 K[3]^3+27}+9\right )^{2/3} K[3]-48 \sqrt [3]{2} \sqrt {3} \left (\sqrt {3} \sqrt {2048 K[3]^3+27}+9\right )^{2/3} K[3]+2\ 3^{2/3} \sqrt {2048 K[3]^3+27} \left (\sqrt {3} \sqrt {2048 K[3]^3+27}+9\right )^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[3]^3+27}+9} K[3]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[3]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[3]^3+27}+9\right )^{2/3}}}+18 \sqrt [6]{3} \left (\sqrt {3} \sqrt {2048 K[3]^3+27}+9\right )^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[3]^3+27}+9} K[3]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[3]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[3]^3+27}+9\right )^{2/3}}}+3\ 6^{2/3} \sqrt {2048 K[3]^3+27} \sqrt [3]{\sqrt {3} \sqrt {2048 K[3]^3+27}+9}+27\ 2^{2/3} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[3]^3+27}+9}}{\left (\sqrt {3} \sqrt {2048 K[3]^3+27}+9\right ) \left (-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[3]^3+27}+9} K[3]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[3]^3+27}+9 \sqrt [3]{2}\right )}}}dK[3]\& \right ]\left [c_1-\frac {x}{12}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{12 K[4]+6^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[4]^3+27}+9} K[4]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[4]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[4]^3+27}+9\right )^{2/3}}}-6 \sqrt [6]{2} \sqrt [12]{3} \sqrt {-\frac {1024\ 2^{2/3} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[4]^3+27}+9} K[4]^3+128 \sqrt [3]{3} \sqrt {2048 K[4]^3+27} K[4]^2+384\ 3^{5/6} K[4]^2-16 \sqrt [3]{2} \sqrt {2048 K[4]^3+27} \left (\sqrt {3} \sqrt {2048 K[4]^3+27}+9\right )^{2/3} K[4]-48 \sqrt [3]{2} \sqrt {3} \left (\sqrt {3} \sqrt {2048 K[4]^3+27}+9\right )^{2/3} K[4]+2\ 3^{2/3} \sqrt {2048 K[4]^3+27} \left (\sqrt {3} \sqrt {2048 K[4]^3+27}+9\right )^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[4]^3+27}+9} K[4]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[4]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[4]^3+27}+9\right )^{2/3}}}+18 \sqrt [6]{3} \left (\sqrt {3} \sqrt {2048 K[4]^3+27}+9\right )^{2/3} \sqrt {\frac {-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[4]^3+27}+9} K[4]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[4]^3+27}+9 \sqrt [3]{2}}{\left (\sqrt {3} \sqrt {2048 K[4]^3+27}+9\right )^{2/3}}}+3\ 6^{2/3} \sqrt {2048 K[4]^3+27} \sqrt [3]{\sqrt {3} \sqrt {2048 K[4]^3+27}+9}+27\ 2^{2/3} \sqrt [6]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[4]^3+27}+9}}{\left (\sqrt {3} \sqrt {2048 K[4]^3+27}+9\right ) \left (-16 \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {2048 K[4]^3+27}+9} K[4]+\sqrt [3]{2} \sqrt {3} \sqrt {2048 K[4]^3+27}+9 \sqrt [3]{2}\right )}}}dK[4]\& \right ]\left [c_1-\frac {x}{12}\right ]\right \}\right \}\]
Maple ✓
cpu = 2.058 (sec), leaf count = 441
\[\left [x +\frac {\ln \left (-14640 \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right )^{3} y \left (x \right )^{6}-39648 \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right )^{2} y \left (x \right )^{7}-36144 \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right ) y \left (x \right )^{8}-11072 y \left (x \right )^{9}-93435 \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right )^{3} y \left (x \right )^{3}-177915 \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right )^{2} y \left (x \right )^{4}-162033 \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right ) y \left (x \right )^{5}-8169 y \left (x \right )^{6}-256 \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right )^{3}+2048 y \left (x \right ) \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right )^{2}-9216 y \left (x \right )^{2} \RootOf \left (\textit {\_Z}^{4}+4 y \left (x \right ) \textit {\_Z}^{3}+6 y \left (x \right )^{2} \textit {\_Z}^{2}+\left (4 y \left (x \right )^{3}-1\right ) \textit {\_Z} +y \left (x \right )^{4}-3 y \left (x \right )\right )+124155 y \left (x \right )^{3}\right )}{9}-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[-(y[x]*(3 - y[x]^3)) - (1 - 4*y[x]^3)*y'[x] + 6*y[x]^2*y'[x]^2 + 4*y[x]*y'[x]^3 + y'[x]^4 == 0,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][(-12*K[1] + 6^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[1]^3] - 16*3^(1/3)*K[1]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(2/3)] - 6*2^(1/6)*3^(1/12)*Sqrt[-((384*3^(5/6)*K[1]^2 + 128*3^(1/3)*K[1]^2*Sqrt[27 + 2048*K[1]^3] + 27*2^(2/3)*3^(1/6)*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(1/3) + 1024*2^(2/3)*3^(1/6)*K[1]^3*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(1/3) + 3*6^(2/3)*Sqrt[27 + 2048*K[1]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(1/3) - 48*2^(1/3)*Sqrt[3]*K[1]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(2/3) - 16*2^(1/3)*K[1]*Sqrt[27 + 2048*K[1]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(2/3) - 18*3^(1/6)*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[1]^3] - 16*3^(1/3)*K[1]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(2/3)] - 2*3^(2/3)*Sqrt[27 + 2048*K[1]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[1]^3] - 16*3^(1/3)*K[1]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(2/3)])/((9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])*(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[1]^3] - 16*3^(1/3)*K[1]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[1]^3])^(1/3))))])^(-1), {K[1], 1, #1}] & ][x/12 + C[1]]}, {y[x] -> InverseFunction[Inactive[Integrate][(-12*K[2] + 6^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[2]^3] - 16*3^(1/3)*K[2]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(2/3)] + 6*2^(1/6)*3^(1/12)*Sqrt[-((384*3^(5/6)*K[2]^2 + 128*3^(1/3)*K[2]^2*Sqrt[27 + 2048*K[2]^3] + 27*2^(2/3)*3^(1/6)*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(1/3) + 1024*2^(2/3)*3^(1/6)*K[2]^3*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(1/3) + 3*6^(2/3)*Sqrt[27 + 2048*K[2]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(1/3) - 48*2^(1/3)*Sqrt[3]*K[2]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(2/3) - 16*2^(1/3)*K[2]*Sqrt[27 + 2048*K[2]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(2/3) - 18*3^(1/6)*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[2]^3] - 16*3^(1/3)*K[2]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(2/3)] - 2*3^(2/3)*Sqrt[27 + 2048*K[2]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[2]^3] - 16*3^(1/3)*K[2]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(2/3)])/((9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])*(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[2]^3] - 16*3^(1/3)*K[2]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[2]^3])^(1/3))))])^(-1), {K[2], 1, #1}] & ][x/12 + C[1]]}, {y[x] -> InverseFunction[Inactive[Integrate][(12*K[3] + 6^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[3]^3] - 16*3^(1/3)*K[3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(2/3)] + 6*2^(1/6)*3^(1/12)*Sqrt[-((384*3^(5/6)*K[3]^2 + 128*3^(1/3)*K[3]^2*Sqrt[27 + 2048*K[3]^3] + 27*2^(2/3)*3^(1/6)*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(1/3) + 1024*2^(2/3)*3^(1/6)*K[3]^3*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(1/3) + 3*6^(2/3)*Sqrt[27 + 2048*K[3]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(1/3) - 48*2^(1/3)*Sqrt[3]*K[3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(2/3) - 16*2^(1/3)*K[3]*Sqrt[27 + 2048*K[3]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(2/3) + 18*3^(1/6)*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[3]^3] - 16*3^(1/3)*K[3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(2/3)] + 2*3^(2/3)*Sqrt[27 + 2048*K[3]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[3]^3] - 16*3^(1/3)*K[3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(2/3)])/((9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])*(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[3]^3] - 16*3^(1/3)*K[3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[3]^3])^(1/3))))])^(-1), {K[3], 1, #1}] & ][-1/12*x + C[1]]}, {y[x] -> InverseFunction[Inactive[Integrate][(12*K[4] + 6^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[4]^3] - 16*3^(1/3)*K[4]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(2/3)] - 6*2^(1/6)*3^(1/12)*Sqrt[-((384*3^(5/6)*K[4]^2 + 128*3^(1/3)*K[4]^2*Sqrt[27 + 2048*K[4]^3] + 27*2^(2/3)*3^(1/6)*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(1/3) + 1024*2^(2/3)*3^(1/6)*K[4]^3*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(1/3) + 3*6^(2/3)*Sqrt[27 + 2048*K[4]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(1/3) - 48*2^(1/3)*Sqrt[3]*K[4]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(2/3) - 16*2^(1/3)*K[4]*Sqrt[27 + 2048*K[4]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(2/3) + 18*3^(1/6)*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[4]^3] - 16*3^(1/3)*K[4]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(2/3)] + 2*3^(2/3)*Sqrt[27 + 2048*K[4]^3]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(2/3)*Sqrt[(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[4]^3] - 16*3^(1/3)*K[4]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(1/3))/(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(2/3)])/((9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])*(9*2^(1/3) + 2^(1/3)*Sqrt[3]*Sqrt[27 + 2048*K[4]^3] - 16*3^(1/3)*K[4]*(9 + Sqrt[3]*Sqrt[27 + 2048*K[4]^3])^(1/3))))])^(-1), {K[4], 1, #1}] & ][-1/12*x + C[1]]}}
Maple raw input
dsolve(diff(y(x),x)^4+4*y(x)*diff(y(x),x)^3+6*y(x)^2*diff(y(x),x)^2-(1-4*y(x)^3)*diff(y(x),x)-(3-y(x)^3)*y(x) = 0, y(x))
Maple raw output
[x+1/9*ln(-14640*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))^3*y(x)^6-39648*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))^2*y(x)^7-36144*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))*y(x)^8-11072*y(x)^9-93435*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))^3*y(x)^3-177915*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))^2*y(x)^4-162033*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))*y(x)^5-8169*y(x)^6-256*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))^3+2048*y(x)*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))^2-9216*y(x)^2*RootOf(_Z^4+4*y(x)*_Z^3+6*y(x)^2*_Z^2+(4*y(x)^3-1)*_Z+y(x)^4-3*y(x))+124155*y(x)^3)-_C1 = 0]