Solve the Initial Value Problem.

Question

dy/dx=2*sec^2*(3x), y(pi/4)=-3 

Answer 1

Separate variables to get dy = 2sec²(3x)dx

 

Integrate both sides to get y = (2/3)tan(3x) + C

 

Since y = 3 when x = π/4, we have 3 = (2/3)tan(3π/4) + C

 

                                                    3 = (2/3)(-1) + C

 

                                                    C = 11/3

 

So, y = (2/3)tan(3x) + 11/3