ODE
\[ y'(x)^3=(y(x)-a)^2 (y(x)-b)^2 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.760204 (sec), leaf count = 236
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ]\left [c_1+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ]\left [c_1-\sqrt [3]{-1} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ]\left [c_1+(-1)^{2/3} x\right ]\right \}\right \}\]
Maple ✓
cpu = 0.187 (sec), leaf count = 133
\[ \left \{ \left ( a-y \left ( x \right ) \right ) \left ( b-y \left ( x \right ) \right ) =0,x-\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt [3]{ \left ( {\it \_a}-a \right ) ^{2} \left ( {\it \_a}-b \right ) ^{2}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!2\,{\frac {1}{ \left ( i\sqrt {3}-1 \right ) \sqrt [3]{ \left ( -{\it \_a}+a \right ) ^{2} \left ( -{\it \_a}+b \right ) ^{2}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-2\,{\frac {1}{ \left ( i\sqrt {3}+1 \right ) \sqrt [3]{ \left ( -{\it \_a}+a \right ) ^{2} \left ( -{\it \_a}+b \right ) ^{2}}}}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y'[x]^3 == (-a + y[x])^2*(-b + y[x])^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[(-3*Hypergeometric2F1[1/3, 2/3, 4/3, (a - #1)/(a - b)]*(a - #1)^(1/3)*((-b + #1)/(a - b))^(2/3))/(b - #1)^(2/3) & ][x + C[1]]}, {y[x] -> InverseFunction[(-3*Hypergeometric2F1[1/3, 2/3, 4/3, (a - #1)/(a - b)]*(a - #1)^(1/3)*((-b + #1)/(a - b))^(2/3))/(b - #1)^(2/3) & ][-((-1)^(1/3)*x) + C[1]]}, {y[x] -> InverseFunction[(-3*Hypergeometric2F1[1/3, 2/3, 4/3, (a - #1)/(a - b)]*(a - #1)^(1/3)*((-b + #1)/(a - b))^(2/3))/(b - #1)^(2/3) & ][(-1)^(2/3)*x + C[1]]}}
Maple raw input
dsolve(diff(y(x),x)^3 = (y(x)-a)^2*(y(x)-b)^2, y(x),'implicit')
Maple raw output
(a-y(x))*(b-y(x)) = 0, x-Intat(1/((_a-a)^2*(_a-b)^2)^(1/3),_a = y(x))-_C1 = 0, x-Intat(-2/(I*3^(1/2)+1)/((-_a+a)^2*(-_a+b)^2)^(1/3),_a = y(x))-_C1 = 0, x-Intat(2/(I*3^(1/2)-1)/((-_a+a)^2*(-_a+b)^2)^(1/3),_a = y(x))-_C1 = 0