ODE
\[ (a+1) x y'(x)+x^2 y''(x)=x^k f\left (x^k y(x),k y(x)+x y'(x)\right ) \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 3.41429 (sec), leaf count = 0 , could not solve
DSolve[(1 + a)*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] == x^k*f[x^k*y[x], k*y[x] + x*Derivative[1][y][x]], y[x], x]
Maple ✗
cpu = 2.769 (sec), leaf count = 0 , could not solve
dsolve(x^2*diff(diff(y(x),x),x)+(1+a)*x*diff(y(x),x) = x^k*f(x^k*y(x),x*diff(y(x),x)+k*y(x)), y(x),'implicit')
Mathematica raw input
DSolve[(1 + a)*x*y'[x] + x^2*y''[x] == x^k*f[x^k*y[x], k*y[x] + x*y'[x]],y[x],x]
Mathematica raw output
DSolve[(1 + a)*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] == x^k*f[x^k*y[x], k*y[x] + x*Derivative[1][y][x]], y[x], x]
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+(1+a)*x*diff(y(x),x) = x^k*f(x^k*y(x),x*diff(y(x),x)+k*y(x)), y(x),'implicit')
Maple raw output
dsolve(x^2*diff(diff(y(x),x),x)+(1+a)*x*diff(y(x),x) = x^k*f(x^k*y(x),x*diff(y(x),x)+k*y(x)), y(x),'implicit')