
First order ode
For the following diferential equation
dy/dx = (2 co^{2}x  sin^{2}x + y^{2})/ 2 cos x , pi/2<x<pi/2
show that the substitution y(x) = sin x + (1/u(x)) yields the deferential equation for u(x),
du/dx = u tanx  (1/2) sec x
Hence find the solution y(x) to the original deferential equation that satisfies the condition
y(0) = 2. Find the interval on which the solution to the initial value problem is defined.
Im having trouble doing this question. I have had about 4 attempts and can not seem to get to the du/dx they have. I'm solving the y= sinx +1/u to give dy/du= cosx u^{2}
and then letting that = the original dy/dx. Is this the way to go about it or am i missing something? i also rearrange the substitution so u= 1/(ysin x).

Re: First order ode
I just realised that we have the exactly same question lol
http://mathhelpforum.com/calculus/22...calculus.html
but I think our method is different, I'm working backward by integrate $\displaystyle \frac{dy}{dx}$ to give me the equation for y, then I also integrate $\displaystyle \frac{du}{dx}$ to get u
so i can sub them into $\displaystyle y(x)=sin(x)+\frac{1}{u(x)}$
look at my link "Prove it" made a reply there, which made sense