ODE
\[ \left (1-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 x \left (1-4 x^2\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )-48 x y(x)+24=0 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 1.36119 (sec), leaf count = 0 , could not solve
DSolve[24 - 48*x*y[x] + (1 - 12*x^2)*(y[x]^2 + 3*Derivative[1][y][x]) + 2*x*(1 - 4*x^2)*(-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x]) == 0, y[x], x]
Maple ✗
cpu = 0.619 (sec), leaf count = 0 , could not solve
dsolve(2*x*(-4*x^2+1)*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)+(-12*x^2+1)*(3*diff(y(x),x)+y(x)^2)-48*x*y(x)+24 = 0, y(x),'implicit')
Mathematica raw input
DSolve[24 - 48*x*y[x] + (1 - 12*x^2)*(y[x]^2 + 3*y'[x]) + 2*x*(1 - 4*x^2)*(-y[x]^3 + y[x]*y'[x] + y''[x]) == 0,y[x],x]
Mathematica raw output
DSolve[24 - 48*x*y[x] + (1 - 12*x^2)*(y[x]^2 + 3*Derivative[1][y][x]) + 2*x*(1 - 4*x^2)*(-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x]) == 0, y[x], x]
Maple raw input
dsolve(2*x*(-4*x^2+1)*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)+(-12*x^2+1)*(3*diff(y(x),x)+y(x)^2)-48*x*y(x)+24 = 0, y(x),'implicit')
Maple raw output
dsolve(2*x*(-4*x^2+1)*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)+(-12*x^2+1)*(3*diff(y(x),x)+y(x)^2)-48*x*y(x)+24 = 0, y(x),'implicit')