Use the differential equation and the given point to find an equation of the function.

Question

The graph of a function f is shown. Use the differential equation and the given point to find an equation of the function.

Answer 1

Step 1 :

The differential equation is .

The point lies on the curve

Integrate the differential function.

Let .

.

Put .

, where C  is an integration constant.

Step 2 :

Evaluation of C :

Substitute the point in the function.

Substitute in

.

Solution :

The function is .