#### 2.545   ODE No. 545

$y'(x)^4-(y(x)-a)^3 (y(x)-b)^2=0$ Mathematica : cpu = 0.664956 (sec), leaf count = 323

$\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ]\left [c_1-\sqrt [4]{-1} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ]\left [c_1+\sqrt [4]{-1} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ]\left [c_1-(-1)^{3/4} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{a-\text {\#1}} \sqrt {\frac {\text {\#1}-b}{a-b}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};\frac {a-\text {\#1}}{a-b}\right )}{\sqrt {b-\text {\#1}}}\& \right ]\left [c_1+(-1)^{3/4} x\right ]\right \}\right \}$ Maple : cpu = 0.122 (sec), leaf count = 144

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