Question

write and solve the differential equation that models the following statment. "the rate if change of W with respect to x is proportional to x+18."

Answer 1

Answer:

$\int k(x + 18)dx = \int kx + 18k dx$ = $k\frac{x^{2} }{2}$ + $18kx$ + C where C is the constant of integration.

Step-by-step explanation:

i)it is given that the rate of change of W with respect to x is proportional to          

     x + 18. Therefore $\frac{dW}{dx}$ = k(x + 18) where k is a constant.

ii) Therefore $\int k(x + 18)dx = \int kx + 18k dx$ = $k\frac{x^{2} }{2}$ + $18kx$ + C where C is the constant of integration.

iii) the complete solution can only be found if we know the constant of proportion and also the constant of integration.