use a graphing utility to graph three solutions, one of which passes through the given point. ds/dθ = tan 2θ, (0, 2)

Question

Slove the differential equation. use a graphing utility to graph three solutions, one of which passes through the given point.

ds/dθ = tan 2θ,    (0, 2)

Answer 1

Step 1:

The function and the point  .

Rewrite .

Integrate the above function.

Step 2:

To calculate the value  we substitute the point in the equation .

Therefore the solution to the differential equation is  .

Step 3:

Consider different values of and plot the graph.

Let us assume as well as .

Obtained function is with .

Graph the function with different values of c.

Solution:

The solution to the differential equation is .