Integration by parts help (I think)

[stereoisomer]

Hey, I''m having trouble integrating this product because it has a a y in it as well as a defined function of x, and I can't find out what y is without integrating, kind of circular. This probably isn't clear and I'm sure it's simple, so here's the problem:

dy/dx = y sec[sup:1x2z7gau]2[/sup:1x2z7gau]x and I'm supposed to find what y(x) is, given that y=5 and x=0

I'm doing this: ? dy/dx dx = y = ? y sec[sup:1x2z7gau]2[/sup:1x2z7gau]x dx

then I'm a little unsure on how to use the formula my teacher taught me with the u's and v's, seeing as I don't know what variable to write the integrals in terms of. I tried

? y dx = y sec[sup:1x2z7gau]2[/sup:1x2z7gau]x - ? sec[sup:1x2z7gau]2[/sup:1x2z7gau]x dx

which doesnt seem like what I should be doing. What should I be doing?

 

[Deleted member 4993]

Hey, I''m having trouble integrating this product because it has a a y in it as well as a defined function of x, and I can't find out what y is without integrating, kind of circular. This probably isn't clear and I'm sure it's simple, so here's the problem:

dy/dx = y sec[sup:m059uz0k]2[/sup:m059uz0k]x and I'm supposed to find what y(x) is, given that y=5 and x=0

I would do the following:

\(\displaystyle \frac{dy}{y} \ = \ sec^2(x)dx\)

\(\displaystyle ln(y) \ = \ tan(x) \ + \ C\)

Now continue....

I'm doing this: ? dy/dx dx = y = ? y sec[sup:m059uz0k]2[/sup:m059uz0k]x dx

then I'm a little unsure on how to use the formula my teacher taught me with the u's and v's, seeing as I don't know what variable to write the integrals in terms of. I tried

? y dx = y sec[sup:m059uz0k]2[/sup:m059uz0k]x - ? sec[sup:m059uz0k]2[/sup:m059uz0k]x dx

which doesnt seem like what I should be doing. What should I be doing?