#### 2.548   ODE No. 548

$y'(x)^6-(y(x)-a)^4 (y(x)-b)^3=0$ Mathematica : cpu = 0.969213 (sec), leaf count = 479

$\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ][c_1-i x]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ][c_1+i x]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ]\left [c_1-\sqrt [6]{-1} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ]\left [c_1+\sqrt [6]{-1} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ]\left [c_1-(-1)^{5/6} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ]\left [c_1+(-1)^{5/6} x\right ]\right \}\right \}$ Maple : cpu = 0.226 (sec), leaf count = 250

$\left \{ x-\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt [6]{ \left ( {\it \_a}-a \right ) ^{4} \left ( {\it \_a}-b \right ) ^{3}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!{\frac {-2\,i}{-\sqrt {3}+i}{\frac {1}{\sqrt [6]{- \left ( -{\it \_a}+a \right ) ^{4} \left ( -{\it \_a}+b \right ) ^{3}}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!{\frac {-2\,i}{\sqrt {3}+i}{\frac {1}{\sqrt [6]{- \left ( -{\it \_a}+a \right ) ^{4} \left ( -{\it \_a}+b \right ) ^{3}}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!{\frac {2\,i}{-\sqrt {3}+i}{\frac {1}{\sqrt [6]{- \left ( -{\it \_a}+a \right ) ^{4} \left ( -{\it \_a}+b \right ) ^{3}}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!{\frac {2\,i}{\sqrt {3}+i}{\frac {1}{\sqrt [6]{- \left ( -{\it \_a}+a \right ) ^{4} \left ( -{\it \_a}+b \right ) ^{3}}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt [6]{- \left ( -{\it \_a}+a \right ) ^{4} \left ( -{\it \_a}+b \right ) ^{3}}}}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =a,y \left ( x \right ) =b \right \}$