ODE No. 548

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

DSolve[-((-a + y[x])^4*(-b + y[x])^3) + Derivative[1][y][x]^6 == 0,y[x],x]
 

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

dsolve(diff(y(x),x)^6-(y(x)-a)^4*(y(x)-b)^3=0,y(x))
 

\[y \left (x \right ) = a\]