2.545   ODE No. 545

\[ y'(x)^4-(y(x)-a)^3 (y(x)-b)^2=0 \] Mathematica : cpu = 0.613965 (sec), leaf count = 323


\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ]\left [-\sqrt [4]{-1} x+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ]\left [\sqrt [4]{-1} x+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ]\left [-(-1)^{3/4} x+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};\frac {a-\text {$\#$1}}{a-b}\right )}{\sqrt {b-\text {$\#$1}}}\& \right ]\left [(-1)^{3/4} x+c_1\right ]\right \}\right \}\] Maple : cpu = 0.217 (sec), leaf count = 144


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