ODE
\[ f(x) (y(x)-a)^5 (y(x)-b)^4+y'(x)^6=0 \] 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 = 1.79746 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 0.918 (sec), leaf count = 434
\[ \left \{ \int ^{y \left ( x \right ) }\!{1 \left ( {\it \_a}-b \right ) ^{-{\frac {2}{3}}} \left ( {\it \_a}-a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+\int ^{x}\!{1\sqrt [6]{f \left ( {\it \_a} \right ) \left ( b-y \left ( x \right ) \right ) ^{4} \left ( a-y \left ( x \right ) \right ) ^{5}} \left ( y \left ( x \right ) -b \right ) ^{-{\frac {2}{3}}} \left ( y \left ( x \right ) -a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+{\it \_C1}=0,\int ^{y \left ( x \right ) }\!{1 \left ( {\it \_a}-b \right ) ^{-{\frac {2}{3}}} \left ( {\it \_a}-a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+\int ^{x}\!-{1\sqrt [6]{f \left ( {\it \_a} \right ) \left ( b-y \left ( x \right ) \right ) ^{4} \left ( a-y \left ( x \right ) \right ) ^{5}} \left ( y \left ( x \right ) -b \right ) ^{-{\frac {2}{3}}} \left ( y \left ( x \right ) -a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+{\it \_C1}=0,\int ^{y \left ( x \right ) }\!{1 \left ( {\it \_a}-b \right ) ^{-{\frac {2}{3}}} \left ( {\it \_a}-a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+\int ^{x}\!-{\frac {i\sqrt {3}-1}{2}\sqrt [6]{f \left ( {\it \_a} \right ) \left ( b-y \left ( x \right ) \right ) ^{4} \left ( a-y \left ( x \right ) \right ) ^{5}} \left ( y \left ( x \right ) -b \right ) ^{-{\frac {2}{3}}} \left ( y \left ( x \right ) -a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+{\it \_C1}=0,\int ^{y \left ( x \right ) }\!{1 \left ( {\it \_a}-b \right ) ^{-{\frac {2}{3}}} \left ( {\it \_a}-a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+\int ^{x}\!{\frac {i\sqrt {3}-1}{2}\sqrt [6]{f \left ( {\it \_a} \right ) \left ( b-y \left ( x \right ) \right ) ^{4} \left ( a-y \left ( x \right ) \right ) ^{5}} \left ( y \left ( x \right ) -b \right ) ^{-{\frac {2}{3}}} \left ( y \left ( x \right ) -a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+{\it \_C1}=0,\int ^{y \left ( x \right ) }\!{1 \left ( {\it \_a}-b \right ) ^{-{\frac {2}{3}}} \left ( {\it \_a}-a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+\int ^{x}\!-{\frac {i\sqrt {3}+1}{2}\sqrt [6]{f \left ( {\it \_a} \right ) \left ( b-y \left ( x \right ) \right ) ^{4} \left ( a-y \left ( x \right ) \right ) ^{5}} \left ( y \left ( x \right ) -b \right ) ^{-{\frac {2}{3}}} \left ( y \left ( x \right ) -a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+{\it \_C1}=0,\int ^{y \left ( x \right ) }\!{1 \left ( {\it \_a}-b \right ) ^{-{\frac {2}{3}}} \left ( {\it \_a}-a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+\int ^{x}\!{\frac {i\sqrt {3}+1}{2}\sqrt [6]{f \left ( {\it \_a} \right ) \left ( b-y \left ( x \right ) \right ) ^{4} \left ( a-y \left ( x \right ) \right ) ^{5}} \left ( y \left ( x \right ) -b \right ) ^{-{\frac {2}{3}}} \left ( y \left ( x \right ) -a \right ) ^{-{\frac {5}{6}}}}{d{\it \_a}}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[f[x]*(-a + y[x])^5*(-b + y[x])^4 + y'[x]^6 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^6+f(x)*(y(x)-a)^5*(y(x)-b)^4 = 0, y(x),'implicit')
Maple raw output
Intat(1/(_a-b)^(2/3)/(_a-a)^(5/6),_a = y(x))+Intat(-(f(_a)*(b-y(x))^4*(a-y(x))^5)^(1/6)/(y(x)-b)^(2/3)/(y(x)-a)^(5/6),_a = x)+_C1 = 0, Intat(1/(_a-b)^(2/3)/(_a-a)^(5/6),_a = y(x))+Intat(1/2*(I*3^(1/2)+1)*(f(_a)*(b-y(x))^4*(a-y(x))^5)^(1/6)/(y(x)-b)^(2/3)/(y(x)-a)^(5/6),_a = x)+_C1 = 0, Intat(1/(_a-b)^(2/3)/(_a-a)^(5/6),_a = y(x))+Intat(-1/2*(I*3^(1/2)-1)*(f(_a)*(b-y(x))^4*(a-y(x))^5)^(1/6)/(y(x)-b)^(2/3)/(y(x)-a)^(5/6),_a = x)+_C1 = 0, Intat(1/(_a-b)^(2/3)/(_a-a)^(5/6),_a = y(x))+Intat(1/2*(I*3^(1/2)-1)*(f(_a)*(b-y(x))^4*(a-y(x))^5)^(1/6)/(y(x)-b)^(2/3)/(y(x)-a)^(5/6),_a = x)+_C1 = 0, Intat(1/(_a-b)^(2/3)/(_a-a)^(5/6),_a = y(x))+Intat(-1/2*(I*3^(1/2)+1)*(f(_a)*(b-y(x))^4*(a-y(x))^5)^(1/6)/(y(x)-b)^(2/3)/(y(x)-a)^(5/6),_a = x)+_C1 = 0, Intat(1/(_a-b)^(2/3)/(_a-a)^(5/6),_a = y(x))+Intat((f(_a)*(b-y(x))^4*(a-y(x))^5)^(1/6)/(y(x)-b)^(2/3)/(y(x)-a)^(5/6),_a = x)+_C1 = 0