4.38.15 $(a+1)x{y}^{\prime }(x)+x^2{y}^{″}(x)=x^{k}f(x^{k}y(x),ky(x)+x{y}^{\prime }(x))$

ODE
$$(a+1)x{y}^{\prime }(x)+x^2{y}^{″}(x)=x^{k}f(x^{k}y(x),ky(x)+x{y}^{\prime }(x))$$ 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')