ODE
\[ y'(x)^4=(y(x)-a)^3 (y(x)-b)^2 \] ODE Classification
[_quadrature]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.73022 (sec), leaf count = 383
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt [4]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} B_{\frac {a-\text {$\#$1}}{a-b}}\left (\frac {1}{4},\frac {1}{2}\right )}{\sqrt {b-\text {$\#$1}} \sqrt [4]{\frac {a-\text {$\#$1}}{a-b}}}\& \right ]\left [c_1-\sqrt [4]{-1} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt [4]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} B_{\frac {a-\text {$\#$1}}{a-b}}\left (\frac {1}{4},\frac {1}{2}\right )}{\sqrt {b-\text {$\#$1}} \sqrt [4]{\frac {a-\text {$\#$1}}{a-b}}}\& \right ]\left [c_1+\sqrt [4]{-1} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt [4]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} B_{\frac {a-\text {$\#$1}}{a-b}}\left (\frac {1}{4},\frac {1}{2}\right )}{\sqrt {b-\text {$\#$1}} \sqrt [4]{\frac {a-\text {$\#$1}}{a-b}}}\& \right ]\left [c_1-(-1)^{3/4} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt [4]{a-\text {$\#$1}} \sqrt {\frac {\text {$\#$1}-b}{a-b}} B_{\frac {a-\text {$\#$1}}{a-b}}\left (\frac {1}{4},\frac {1}{2}\right )}{\sqrt {b-\text {$\#$1}} \sqrt [4]{\frac {a-\text {$\#$1}}{a-b}}}\& \right ]\left [c_1+(-1)^{3/4} x\right ]\right \}\right \}\]
Maple ✓
cpu = 0.175 (sec), leaf count = 144
\[ \left \{ x-\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt [4]{ \left ( {\it \_a}-a \right ) ^{3} \left ( {\it \_a}-b \right ) ^{2}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!{-i{\frac {1}{\sqrt [4]{- \left ( -{\it \_a}+a \right ) ^{3} \left ( -{\it \_a}+b \right ) ^{2}}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!{i{\frac {1}{\sqrt [4]{- \left ( -{\it \_a}+a \right ) ^{3} \left ( -{\it \_a}+b \right ) ^{2}}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt [4]{- \left ( -{\it \_a}+a \right ) ^{3} \left ( -{\it \_a}+b \right ) ^{2}}}}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =a,y \left ( x \right ) =b \right \} \] Mathematica raw input
DSolve[y'[x]^4 == (-a + y[x])^3*(-b + y[x])^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[-((Beta[(a - #1)/(a - b), 1/4, 1/2]*(a - #1)^(1/4)*Sqrt[(-b + #1)/(a - b)])/(((a - #1)/(a - b))^(1/4)*Sqrt[b - #1])) & ][-((-1)^(1/4)*x) + C[1]]}, {y[x] -> InverseFunction[-((Beta[(a - #1)/(a - b), 1/4, 1/2]*(a - #1)^(1/4)*Sqrt[(-b + #1)/(a - b)])/(((a - #1)/(a - b))^(1/4)*Sqrt[b - #1])) & ][(-1)^(1/4)*x + C[1]]}, {y[x] -> InverseFunction[-((Beta[(a - #1)/(a - b), 1/4, 1/2]*(a - #1)^(1/4)*Sqrt[(-b + #1)/(a - b)])/(((a - #1)/(a - b))^(1/4)*Sqrt[b - #1])) & ][-((-1)^(3/4)*x) + C[1]]}, {y[x] -> InverseFunction[-((Beta[(a - #1)/(a - b), 1/4, 1/2]*(a - #1)^(1/4)*Sqrt[(-b + #1)/(a - b)])/(((a - #1)/(a - b))^(1/4)*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),'implicit')
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