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## Homework Statement

Which of the methods of finding analytic solutions of differential equations

could you use to solve this equation? Give reasons for

your answer.

a

[tex]y+\frac{dy}{dx}tan(x) = 2 (\pi/4 \leq x < \pi/2)[/tex]

b

[tex]\sqrt{t^2+9}\frac{dy}{dx}=y^2 (0<y)[/tex]

## The Attempt at a Solution

The integrating factor method for both, the initial value part I dont have a problem with,

For part a, I hit a wall when it came to integrating for the solution

I got g(x)=1, and h(x)=2/tan(x)

the integrating factor I got as p(x)=exp(x)

Putting it all back together I came unstuck here

[tex]exp(x)y=\int{exp(x)2cot(x)} dx[/tex]

Mainly because to get the same answer as wolphram alpha, I had to use the exp funion on the RHS to get rid of the LN that came from integrating the cotangent. Meaning then that I cant eliminate the exp from the LHS. So im confused and havent attempted part b yet, but I think it is also to be solved in the same way.