The following questions i need help on:
Solve the Differential Equations
u=2x du=2 dx
what should i do next?
i tried but that didn't work.
Your algebra for (1) is incorrect. As far as I can tell, your mistake was in going from step 1 to step 2. Try this:
As for the second problem, your answer and the book's answer are equivalent. You've just re-defined your constant of integration once or twice. Your constant is the negative of the book's constant. That is an unimportant difference.
As for #3, raj007's solution is a bit bizarre, in my opinion. I would go with a straight-forward trig substitution, or look the integral up in a table if you're allowed to do that.
That looks good, except that in going from step 3 to 4, you lost your y-1 factor. And then in going from step 4 to step 5, you regained it! I wouldn't recommend dropping terms willy-nilly, unless you have a good reason for doing it (approximation, for example).
Recommendation: rename your constant of integration so it looks a bit cleaner. That is, define, say, K = exp(2C), and use K in both places there. This is not a fundamentally important aspect of the problem, however. It is merely cosmetic.