2(1 − x)x(1 − y(x))(x − y(x))y(x)y′′(x) = f(x)((1−y(x))(x−y(x))y(x))3∕2+2(1−y(x))( x2 − 2xy(x) + y(x)) y(x)y′(x)+(1−x)x( 3y(x)2 − 2xy(x) − 2y(x) + x) y′(x)2−( ( 1 −y(x)2) y(x)2)

4.41.36 $2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=f(x) ((1-y(x)) (x-y(x)) y(x))^{3/2}+2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (\left (1-y(x)^2\right ) y(x)^2\right )$

ODE
\[ 2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=f(x) ((1-y(x)) (x-y(x)) y(x))^{3/2}+2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (\left (1-y(x)^2\right ) y(x)^2\right ) \] ODE Classiﬁcation

odeadvisor timed out

Book solution method
TO DO

Mathematica ✗
cpu = 618.953 (sec), leaf count = 0 , timed out

$Aborted

Maple ✗
cpu = 0. (sec), leaf count = 0 , hanged

dsolve(2*x*y(x)*(1-x)*(1-y(x))*(x-y(x))*diff(diff(y(x),x),x) = x*(1-x)*(x-2*x*y(x)-2*y(x)+3*y(x)^2)*diff(y(x),x)^2+2*y(x)*(1-y(x))*(x^2+y(x)-2*x*y(x))*diff(y(x),x)-y(x)^2*(1-y(x)^2)+f(x)*(y(x)*(1-y(x))*(x-y(x)))^(3/2), y(x))

Mathematica raw input

DSolve[2*(1 - x)*x*(1 - y[x])*(x - y[x])*y[x]*y''[x] == f[x]*((1 - y[x])*(x - y[x])*y[x])^(3/2) - y[x]^2*(1 - y[x]^2) + 2*(1 - y[x])*y[x]*(x^2 + y[x] - 2*x*y[x])*y'[x] + (1 - x)*x*(x - 2*y[x] - 2*x*y[x] + 3*y[x]^2)*y'[x]^2,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

Maple raw output

dsolve(2*x*y(x)*(1-x)*(1-y(x))*(x-y(x))*diff(diff(y(x),x),x) = x*(1-x)*(x-2*x*y(
x)-2*y(x)+3*y(x)^2)*diff(y(x),x)^2+2*y(x)*(1-y(x))*(x^2+y(x)-2*x*y(x))*diff(y(x)
,x)-y(x)^2*(1-y(x)^2)+f(x)*(y(x)*(1-y(x))*(x-y(x)))^(3/2), y(x))

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4.41.36 \(2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=f(x) ((1-y(x)) (x-y(x)) y(x))^{3/2}+2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (\left (1-y(x)^2\right ) y(x)^2\right )\)