ODE
\[ (1-y(x))^3 \left (\text {a0}+\text {a1} y(x)^2\right )+\text {a2} x (1-y(x)) y(x)^2+\text {a3} x^3 y(x)^2 (y(x)+1)+2 x^2 (1-y(x)) y(x) y''(x)-x^2 (1-3 y(x)) y'(x)^2+2 x (1-y(x)) y(x) y'(x)=0 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 15.6341 (sec), leaf count = 0 , could not solve
DSolve[a2*x*(1 - y[x])*y[x]^2 + a3*x^3*y[x]^2*(1 + y[x]) + (1 - y[x])^3*(a0 + a1*y[x]^2) + 2*x*(1 - y[x])*y[x]*Derivative[1][y][x] - x^2*(1 - 3*y[x])*Derivative[1][y][x]^2 + 2*x^2*(1 - y[x])*y[x]*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 3.96 (sec), leaf count = 0 , could not solve
dsolve(2*x^2*y(x)*(1-y(x))*diff(diff(y(x),x),x)-x^2*(1-3*y(x))*diff(y(x),x)^2+2*x*y(x)*(1-y(x))*diff(y(x),x)+(a0+a1*y(x)^2)*(1-y(x))^3+a2*x*y(x)^2*(1-y(x))+a3*x^3*y(x)^2*(1+y(x)) = 0, y(x))
Mathematica raw input
DSolve[a2*x*(1 - y[x])*y[x]^2 + a3*x^3*y[x]^2*(1 + y[x]) + (1 - y[x])^3*(a0 + a1*y[x]^2) + 2*x*(1 - y[x])*y[x]*y'[x] - x^2*(1 - 3*y[x])*y'[x]^2 + 2*x^2*(1 - y[x])*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[a2*x*(1 - y[x])*y[x]^2 + a3*x^3*y[x]^2*(1 + y[x]) + (1 - y[x])^3*(a0 + a1*y[x]^2) + 2*x*(1 - y[x])*y[x]*Derivative[1][y][x] - x^2*(1 - 3*y[x])*Derivative[1][y][x]^2 + 2*x^2*(1 - y[x])*y[x]*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(2*x^2*y(x)*(1-y(x))*diff(diff(y(x),x),x)-x^2*(1-3*y(x))*diff(y(x),x)^2+2*x*y(x)*(1-y(x))*diff(y(x),x)+(a0+a1*y(x)^2)*(1-y(x))^3+a2*x*y(x)^2*(1-y(x))+a3*x^3*y(x)^2*(1+y(x)) = 0, y(x))
Maple raw output
dsolve(2*x^2*y(x)*(1-y(x))*diff(diff(y(x),x),x)-x^2*(1-3*y(x))*diff(y(x),x)^2+2*x*y(x)*(1-y(x))*diff(y(x),x)+(a0+a1*y(x)^2)*(1-y(x))^3+a2*x*y(x)^2*(1-y(x))+a3*x^3*y(x)^2*(1+y(x)) = 0, y(x))