2.548   ODE No. 548

\[ y'(x)^6-(y(x)-a)^4 (y(x)-b)^3=0 \] Mathematica : cpu = 0.93247 (sec), leaf count = 479


\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ][c_1-i x]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ][i x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ]\left [-\sqrt [6]{-1} x+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ]\left [\sqrt [6]{-1} x+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ]\left [-(-1)^{5/6} x+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ]\left [(-1)^{5/6} x+c_1\right ]\right \}\right \}\] Maple : cpu = 0.451 (sec), leaf count = 250


\[y \relax (x ) = a\]