ODE
\[ 2 (1-x)^2 x^2 (1-y(x)) (x-y(x)) y(x) y''(x)=\text {a0} x (x-y(x))^2 (1-y(x))^2+\text {a1} (1-x) (x-y(x))^2 y(x)^2+(\text {a2}-1) (1-x) x y(x)^2 (1-y(x))^2+\text {a3} (x-y(x))^2 y(x)^2 (1-y(x))^2+2 (1-x) x y(x) \left (x^2-2 x y(x)+y(x)\right ) (1-y(x))^2 y'(x)+(1-x)^2 x^2 \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 27.7066 (sec), leaf count = 0 , could not solve
DSolve[2*(1 - x)^2*x^2*(1 - y[x])*(x - y[x])*y[x]*Derivative[2][y][x] == a0*x*(1 - y[x])^2*(x - y[x])^2 + (-1 + a2)*(1 - x)*x*(1 - y[x])^2*y[x]^2 + a1*(1 - x)*(x - y[x])^2*y[x]^2 + a3*(1 - y[x])^2*(x - y[x])^2*y[x]^2 + 2*(1 - x)*x*(1 - y[x])^2*y[x]*(x^2 + y[x] - 2*x*y[x])*Derivative[1][y][x] + (1 - x)^2*x^2*(x - 2*y[x] - 2*x*y[x] + 3*y[x]^2)*Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 0. (sec), leaf count = 0 , hanged
dsolve(2*x^2*y(x)*(1-x)^2*(1-y(x))*(x-y(x))*diff(diff(y(x),x),x) = x^2*(1-x)^2*(x-2*x*y(x)-2*y(x)+3*y(x)^2)*diff(y(x),x)^2+2*x*y(x)*(1-x)*(1-y(x))^2*(x^2+y(x)-2*x*y(x))*diff(y(x),x)+a0*x*(1-y(x))^2*(x-y(x))^2+a1*(1-x)*y(x)^2*(x-y(x))^2+(a2-1)*x*y(x)^2*(1-x)*(1-y(x))^2+a3*y(x)^2*(x-y(x))^2*(1-y(x))^2, y(x),'implicit')
Mathematica raw input
DSolve[2*(1 - x)^2*x^2*(1 - y[x])*(x - y[x])*y[x]*y''[x] == a0*x*(1 - y[x])^2*(x - y[x])^2 + (-1 + a2)*(1 - x)*x*(1 - y[x])^2*y[x]^2 + a1*(1 - x)*(x - y[x])^2*y[x]^2 + a3*(1 - y[x])^2*(x - y[x])^2*y[x]^2 + 2*(1 - x)*x*(1 - y[x])^2*y[x]*(x^2 + y[x] - 2*x*y[x])*y'[x] + (1 - x)^2*x^2*(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)^2*x^2*(1 - y[x])*(x - y[x])*y[x]*Derivative[2][y][x] == a0*x*(1 - y[x])^2*(x - y[x])^2 + (-1 + a2)*(1 - x)*x*(1 - y[x])^2*y[x]^2 + a1*(1 - x)*(x - y[x])^2*y[x]^2 + a3*(1 - y[x])^2*(x - y[x])^2*y[x]^2 + 2*(1 - x)*x*(1 - y[x])^2*y[x]*(x^2 + y[x] - 2*x*y[x])*Derivative[1][y][x] + (1 - x)^2*x^2*(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^2*y(x)*(1-x)^2*(1-y(x))*(x-y(x))*diff(diff(y(x),x),x) = x^2*(1-x)^2*(x-2*x*y(x)-2*y(x)+3*y(x)^2)*diff(y(x),x)^2+2*x*y(x)*(1-x)*(1-y(x))^2*(x^2+y(x)-2*x*y(x))*diff(y(x),x)+a0*x*(1-y(x))^2*(x-y(x))^2+a1*(1-x)*y(x)^2*(x-y(x))^2+(a2-1)*x*y(x)^2*(1-x)*(1-y(x))^2+a3*y(x)^2*(x-y(x))^2*(1-y(x))^2, y(x),'implicit')
Maple raw output
dsolve(2*x^2*y(x)*(1-x)^2*(1-y(x))*(x-y(x))*diff(diff(y(x),x),x) = x^2*(1-x)^2*(x-2*x*y(x)-2*y(x)+3*y(x)^2)*diff(y(x),x)^2+2*x*y(x)*(1-x)*(1-y(x))^2*(x^2+y(x)-2*x*y(x))*diff(y(x),x)+a0*x*(1-y(x))^2*(x-y(x))^2+a1*(1-x)*y(x)^2*(x-y(x))^2+(a2-1)*x*y(x)^2*(1-x)*(1-y(x))^2+a3*y(x)^2*(x-y(x))^2*(1-y(x))^2, y(x),'implicit')