ODE
\[ 2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=f(x) ((1-y(x)) (x-y(x)) y(x))^{3/2}+2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (1-y(x)^2\right ) y(x)^2 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 153.004 (sec), leaf count = 0 , could not solve
DSolve[2*(1 - x)*x*(1 - y[x])*(x - y[x])*y[x]*Derivative[2][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])*Derivative[1][y][x] + (1 - x)*x*(x - 2*y[x] - 2*x*y[x] + 3*y[x]^2)*Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 2.211 (sec), leaf count = 0 , exception
time expired
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
DSolve[2*(1 - x)*x*(1 - y[x])*(x - y[x])*y[x]*Derivative[2][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])*Derivative[1][y][x] + (1 - x)*x*(x - 2*y[x] - 2*x*y[x] + 3*y[x]^2)*Derivative[1][y][x]^2, y[x], x]
Maple raw input
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),'implicit')
Maple raw output
time expired