1. ## initial value problems

I'm either missing something, or my book has incorrect answers...

$\frac{dy}{dx} = 4e^x; y(2) = \pi$

integrating gets...

$y = 4e^x + C$

$y(2) = \pi = 4e^{(2)} + C$
$C = \pi - 4e^{(2)} = -26.4$

Thus $y = 4e^x -26.4$
Is this correct? My book says $y = 4e^x -4 + \pi$.

Looks like they used $e^0$.

The other one...

$\frac{d^2w}{dt^2} = \sqrt{t} = t^{1/2}; w'(1) = -2, w(1) = 2$

$w' = \frac{2}{3}t^{3/2} + C_1$
$w'(1) = -2 = \frac{2}{3}(1)^{3/2} + C_1$
$C_1 = -\frac{8}{3}$

$w = \frac{4}{15}t^{5/2} - \frac{8}{3}t + C_2$
$w(1) = 2 = \frac{4}{15}(1)^{5/2} - \frac{8}{3}(1) + C_2$
$C_2 = \frac{22}{5}$

$w = \frac{4}{15}t^{5/2} - \frac{8}{3}t + \frac{22}{5}$

Correct?

Book says: $w = 4t^{5/2} - 2t +2$

-Scott

2. Just substitute it into the equation to see if it works. What is so hard?

3. Originally Posted by ThePerfectHacker
Just substitute it into the equation to see if it works. What is so hard?
Well, it didn't seem hard at all. But, I'm studying this on my own, no teacher or class mates, just me and a book. So when my answers differed so much from the book, I just wanted to check if I was on-track, or totally derailed.

-Scott