Thread: Calculus quiz tomorrow..help with this one review problem?

Solve initial value problem using sep. of variables

y(prime)=cos^2(x) y(0)=pi/4

I ended up using integration by parts and got to here:

y=cosx * sinx - x + C

and C= pi/4

but the book says the answer is:

y=.5(x+.5sin(2x))+pi/4

what did I do wrong?

Originally Posted by woohoo

Solve initial value problem using sep. of variables

y(prime)=cos^2(x) y(0)=pi/4

I ended up using integration by parts and got to here:

y=cosx * sinx - x + C

and C= pi/4

but the book says the answer is:

y=.5(x+.5sin(2x))+pi/4

what did I do wrong?

Use the identity .

So



Since ,





So .

Okay I understand the book's answer now.

But I don't get why my method turned out incorrect.

I got to where y= integral (cos^2(x) dx)=integral (cosx * cosx dx)

using separation by parts:

y=cosxsinx-integral(x)=cosxsinx-x+C

where did I go wrong?

Nevermind.

I figure out where I went wrong.

Thanks!

Originally Posted by woohoo

Okay I understand the book's answer now.

But I don't get why my method turned out incorrect.

I got to where y= integral (cos^2(x) dx)=integral (cosx * cosx dx)

using separation by parts:

y=cosxsinx-integral(x)=cosxsinx-x+C

where did I go wrong?

Are you trying to do separation of variables or integration by parts? They're two different methods.

You only use separation of variables if you have a Separable linear DE, which you don't, so I guess you're trying to do integration by parts...

Integration by parts is as follows...

.

So if you're integrating , then and . So what are and ?

In this case you should end up with ... not fun to work with as it's just as bad as . Just use the trig identity.