1. For which values of k is the polynomial y = x^k a solution of the dierential equation

d^2y/dx^2 = 20 (y/x^2)?

Enter these values in the box below, separating them with a semicolon if there is more than one.

2.

Solve the problem with the following initial value:

dy/dx = 1 + y^2/(x + 3)^5, y (-2) = 0.

Give an exact formula for y.

3.We want to solve the differential equation dy/dx = xe^2x + y^5/ y^4 This differential equation is separable and can be expressed in the form. N (y) dy = M (x) dx, a) M(x) = N(y) = b) To calculate the integral N (y) dy, we must use the substitution u = n(u) = we find that n(u)du = + K n(y)dy =. +k