ODE
\[ y'(x)^4=(y(x)-a)^3 (y(x)-b)^2 \] ODE Classification
[_quadrature]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.892348 (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 = 0.339 (sec), leaf count = 141
\[\left [y \left (x \right ) = a, y \left (x \right ) = b, x -\left (\int _{}^{y \left (x \right )}\frac {1}{\left (\left (\textit {\_a} -a \right )^{3} \left (\textit {\_a} -b \right )^{2}\right )^{\frac {1}{4}}}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}\frac {i}{\left (\left (\textit {\_a} -a \right )^{3} \left (\textit {\_a} -b \right )^{2}\right )^{\frac {1}{4}}}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}-\frac {i}{\left (\left (\textit {\_a} -a \right )^{3} \left (\textit {\_a} -b \right )^{2}\right )^{\frac {1}{4}}}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}-\frac {1}{\left (\left (\textit {\_a} -a \right )^{3} \left (\textit {\_a} -b \right )^{2}\right )^{\frac {1}{4}}}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y'[x]^4 == (-a + y[x])^3*(-b + y[x])^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[(-4*Hypergeometric2F1[1/4, 1/2, 5/4, (a - #1)/(a - b)]*(a - #1)^(1/4)*Sqrt[(-b + #1)/(a - b)])/Sqrt[b - #1] & ][-((-1)^(1/4)*x) + C[1]]}, {y[x] -> InverseFunction[(-4*Hypergeometric2F1[1/4, 1/2, 5/4, (a - #1)/(a - b)]*(a - #1)^(1/4)*Sqrt[(-b + #1)/(a - b)])/Sqrt[b - #1] & ][(-1)^(1/4)*x + C[1]]}, {y[x] -> InverseFunction[(-4*Hypergeometric2F1[1/4, 1/2, 5/4, (a - #1)/(a - b)]*(a - #1)^(1/4)*Sqrt[(-b + #1)/(a - b)])/Sqrt[b - #1] & ][-((-1)^(3/4)*x) + C[1]]}, {y[x] -> InverseFunction[(-4*Hypergeometric2F1[1/4, 1/2, 5/4, (a - #1)/(a - b)]*(a - #1)^(1/4)*Sqrt[(-b + #1)/(a - b)])/Sqrt[b - #1] & ][(-1)^(3/4)*x + C[1]]}}
Maple raw input
dsolve(diff(y(x),x)^4 = (y(x)-a)^3*(y(x)-b)^2, y(x))
Maple raw output
[y(x) = a, y(x) = b, x-Intat(1/((_a-a)^3*(_a-b)^2)^(1/4),_a = y(x))-_C1 = 0, x-Intat(I/((_a-a)^3*(_a-b)^2)^(1/4),_a = y(x))-_C1 = 0, x-Intat(-I/((_a-a)^3*(_a-b)^2)^(1/4),_a = y(x))-_C1 = 0, x-Intat(-1/((_a-a)^3*(_a-b)^2)^(1/4),_a = y(x))-_C1 = 0]