Question

Let =f() be the solution satisfying the differential equation dy/dx = k(14+) where f(0)=9 and f(3)=13. What is the value of f()?

Answer 1

To find the value of f(x), you need to solve the given differential equation dy/dx = k(14+x) with the initial conditions f(0) = 9 and f(3) = 13. However, because k is undefined, we cannot determine the value of f(x) based on the given information.

Step-by-step explanation:

To find the value of f(x), we need to solve the given differential equation dy/dx = k(14+x) with the initial conditions f(0) = 9 and f(3) = 13.

1. Integrate both sides of the equation with respect to x to get f(x). The integral of k(14+x) with respect to x is k(14x + (x^2)/2).
2. Apply the initial condition f(0) = 9 to find the value of k. Substituting x = 0 and f(x) = 9 into the equation f(x) = k(14x + (x^2)/2), we get 9 = k(0 + 0). Therefore, k = 9/0 which is undefined.
3. Since k is undefined, we cannot determine the value of f(x) based on the given information.