# Math Help - DE question

1. ## DE question

im doing my DE HW and i dont understand how the book came out with an answer.. This is separable variables with an initial value.

(dx/dt) = 4(x^2+1) the intial value is: x((pi)/4)=1

the answer is: y= sin ((1/2)x^2+c)

and i have no idea where the sin came from...i know im probaly missing a rule somewhere, thanks for any help to get the jucices going!

2. Originally Posted by neven87
im doing my DE HW and i dont understand how the book came out with an answer.. This is separable variables with an initial value.

(dx/dt) = 4(x^2+1) the intial value is: x((pi)/4)=1

the answer is: y= sin ((1/2)x^2+c)

and i have no idea where the sin came from...i know im probaly missing a rule somewhere, thanks for any help to get the jucices going!
be sure you don't have a typo here, or that you are looking at the right question. because as the question is stated, your answer should be of the form x = f(t) not y = f(x)

the answer i got is $x = \tan \left( 4t - \frac {3 \pi}{4} \right)$

3. And what's that c in the answer?
Thought it was an IVP...

I get the same answer as jhevon.

4. Originally Posted by neven87
(dx/dt) = 4(x^2+1) the intial value is: x((pi)/4)=1
$\frac{1}{1+x^2} \cdot x' = 4$

$\int \frac{1}{1+x^2} x' \ dt = \int 4 dt$

$\tan^{-1} x = 4t+C$

$x = \tan (4t+C)$

5. It was a misprint the answer is x= tan(4t-3/4(pi))

6. AH! missed the inverse tangent...thanks!