Hi its me again and I have return with more question that I currently got stuck on

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For the following differential equation

,

show that the substitution , yields the differential equation for

Hence find the solution to the original differential equation that satisfies the condition . Find the interval on which the solution to the initial value problem is defined.

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So I first set out to integrate first, however I have a problem that I do not know how to move to the otherside of the equation

e.g.

what I did is

I integrated by using integration by parts with u=tan(x) and

so the equation become

+ C

I'm certain that my integration is wrong, since y(0)=2 will result in

The same problem also applies to

since I do not know how to move, the and to the other side of the equation. So can any body tell me how to integrate this question?

Thanks

Junks

P.S. I finally posted this in latex

edit: I'll try to use First Order, O.D.E but since will first order O,D,E work there?

By first order O.D. E

I found my to be

is this correct?