Solve Integral Problem: dy/dx=7sec^2(pix/4)tan(pix/4), y'(1)=0, y(1)=5

[Chas3down]

Homework Statement

d2y/dx2 = 7sec^2(pix/4)tan(pix/4)
y'(1)=0
y(1)=5

Homework Equations

The Attempt at a Solution

dy/dx = 14/pi sec^2(pix/4)-28/pi
y = 56tan(pix/4)/pi^2-28x/pi+5-56/pi^2+28/pi


Not sure where I went wrong, but I checked on my calc and it wasn't equal.

 

[dirk_mec1]

The first derative should be something with tan^2(..).

 

[Chas3down]

1 + tan^2(...) = sec^2(...) but 1 is just part of c

EDIT:

dy/dx = 14/pi tan^2(pix/4) - 14/pi

y = 56tan(pix/4)/pi^2 - 56(pix/4)/pi^2 - 14x/pi + 5 - 56/pi^2 + 28/picould anyone check this please?

 

[haruspex]

1 + tan^2(...) = sec^2(...) but 1 is just part of c

EDIT:

dy/dx = 14/pi tan^2(pix/4) - 14/pi

y = 56tan(pix/4)/pi^2 - 56(pix/4)/pi^2 - 14x/pi + 5 - 56/pi^2 + 28/pi


could anyone check this please?

Looks right, but you can simplify a little. Two terms are the same.