ODE
\[ f(x) (y(x)-a)^2 (y(x)-b)^2+y'(x)^3=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
Book solution method
Binomial equation \((y')^m + F(x) G(y)=0\)
Mathematica ✓
cpu = 0.746532 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 1.83 (sec), leaf count = 212
\[\left [\int _{}^{y \left (x \right )}\frac {1}{\left (\left (-\textit {\_a} +a \right ) \left (-\textit {\_a} +b \right )\right )^{\frac {2}{3}}}d \textit {\_a} +\int _{}^{x}-\frac {\left (-f \left (\textit {\_a} \right ) \left (a -y \left (x \right )\right )^{2} \left (b -y \left (x \right )\right )^{2}\right )^{\frac {1}{3}}}{\left (\left (a -y \left (x \right )\right ) \left (b -y \left (x \right )\right )\right )^{\frac {2}{3}}}d \textit {\_a} +\textit {\_C1} = 0, \int _{}^{y \left (x \right )}\frac {1}{\left (\left (-\textit {\_a} +a \right ) \left (-\textit {\_a} +b \right )\right )^{\frac {2}{3}}}d \textit {\_a} +\int _{}^{x}\frac {\left (-f \left (\textit {\_a} \right ) \left (a -y \left (x \right )\right )^{2} \left (b -y \left (x \right )\right )^{2}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2 \left (\left (a -y \left (x \right )\right ) \left (b -y \left (x \right )\right )\right )^{\frac {2}{3}}}d \textit {\_a} +\textit {\_C1} = 0, \int _{}^{y \left (x \right )}\frac {1}{\left (\left (-\textit {\_a} +a \right ) \left (-\textit {\_a} +b \right )\right )^{\frac {2}{3}}}d \textit {\_a} +\int _{}^{x}-\frac {\left (-f \left (\textit {\_a} \right ) \left (a -y \left (x \right )\right )^{2} \left (b -y \left (x \right )\right )^{2}\right )^{\frac {1}{3}} \left (-1+i \sqrt {3}\right )}{2 \left (\left (a -y \left (x \right )\right ) \left (b -y \left (x \right )\right )\right )^{\frac {2}{3}}}d \textit {\_a} +\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[f[x]*(-a + y[x])^2*(-b + y[x])^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3+f(x)*(y(x)-a)^2*(y(x)-b)^2 = 0, y(x))
Maple raw output
[Intat(1/((-_a+a)*(-_a+b))^(2/3),_a = y(x))+Intat(-(-f(_a)*(a-y(x))^2*(b-y(x))^2)^(1/3)/((a-y(x))*(b-y(x)))^(2/3),_a = x)+_C1 = 0, Intat(1/((-_a+a)*(-_a+b))^(2/3),_a = y(x))+Intat(1/2*(-f(_a)*(a-y(x))^2*(b-y(x))^2)^(1/3)*(1+I*3^(1/2))/((a-y(x))*(b-y(x)))^(2/3),_a = x)+_C1 = 0, Intat(1/((-_a+a)*(-_a+b))^(2/3),_a = y(x))+Intat(-1/2*(-f(_a)*(a-y(x))^2*(b-y(x))^2)^(1/3)*(-1+I*3^(1/2))/((a-y(x))*(b-y(x)))^(2/3),_a = x)+_C1 = 0]