Differential equation initial value prob

[-EquinoX-]

Homework Statement

http://img16.imageshack.us/img16/1008/questionsh.th.jpg

Homework Equations

The Attempt at a Solution

My question is that should we divide each side by sin(t) first? Because I tried dividing it with sin(t) and then I have u(x) = exp(csc(x)), which is kind of hard to integrate.

Reason why I divide it by sin(t) is to get the following factor

y' + p(x)y = q(x)

and u(x) = exp(integral of p(x) dx)

please correct me steps ehre

 

[rock.freak667]

yes divide by sin(t)



$$\int \frac{cost}{sint} dt$$

notice that d/dt(sint)= cost ?

 

[-EquinoX-]

yes divide by sin(t)
$$\int \frac{cost}{sint} dt$$

notice that d/dt(sint)= cost ?

This will be equal to:

$$\int cot(t) dt$$

which is:

$${-(csc(t))}^2$$

and so u(x) is e^(csc(t))

 

[CharmedQuark]

remember the formula for d/dx(ln x)

d/dx(ln x)= x'/x

separate cot into cos/sin.