Question

Determine the number k so that there is a solution to the differential equation ky'- y = x that satisfies the conditions y(1) = 0 and y'(1) = 1

Answer 1

To solve for k, we first take the derivative of the differential equation to obtain:

ky'' - y' = 1

Then we substitute y = 0 and y' = 1 when x = 1, giving us:

k(1) - (1) = 1

k = 2

Therefore, the value of k that satisfies the given conditions is k = 2.