ODE
\[ a x y(x)+b-\left (k x^{k-1}-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 \left (x^k-4 x^3\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )=0 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 5.158 (sec), leaf count = 0 , could not solve
DSolve[b + a*x*y[x] - (-12*x^2 + k*x^(-1 + k))*(y[x]^2 + 3*Derivative[1][y][x]) + 2*(-4*x^3 + x^k)*(-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x]) == 0, y[x], x]
Maple ✗
cpu = 3.817 (sec), leaf count = 0 , could not solve
dsolve(2*(x^k-4*x^3)*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)-(k*x^(k-1)-12*x^2)*(3*diff(y(x),x)+y(x)^2)+a*x*y(x)+b = 0, y(x),'implicit')
Mathematica raw input
DSolve[b + a*x*y[x] - (-12*x^2 + k*x^(-1 + k))*(y[x]^2 + 3*y'[x]) + 2*(-4*x^3 + x^k)*(-y[x]^3 + y[x]*y'[x] + y''[x]) == 0,y[x],x]
Mathematica raw output
DSolve[b + a*x*y[x] - (-12*x^2 + k*x^(-1 + k))*(y[x]^2 + 3*Derivative[1][y][x]) + 2*(-4*x^3 + x^k)*(-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x]) == 0, y[x], x]
Maple raw input
dsolve(2*(x^k-4*x^3)*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)-(k*x^(k-1)-12*x^2)*(3*diff(y(x),x)+y(x)^2)+a*x*y(x)+b = 0, y(x),'implicit')
Maple raw output
dsolve(2*(x^k-4*x^3)*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)-(k*x^(k-1)-12*x^2)*(3*diff(y(x),x)+y(x)^2)+a*x*y(x)+b = 0, y(x),'implicit')