# Thread: confirmation in regards to this question

1. ## confirmation in regards to this question

Hi all,

I recently posted 'want some confirmation' and it was in relation this question:

dy/dx = (5x^2)(cos^2(y)) for y(1) = 5*pi

i get y = arctan[ 5/3 (x^3 -1)]

however the answer states y = arctan[5/3 (x^3 -1)] + 5*pi...

I have no idea where that 5*pi is coming from hence it lead to the post earlier.

Thanks in advance,
ArTiCk

2. Originally Posted by ArTiCK
Hi all,

I recently posted 'want some confirmation' and it was in relation this question:

dy/dx = (5x^2)(cos^2(y)) for y(1) = 5*pi

i get y = arctan[ 5/3 (x^3 -1)]

however the answer states y = arctan[5/3 (x^3 -1)] + 5*pi...

I have no idea where that 5*pi is coming from hence it lead to the post earlier.

Thanks in advance,
ArTiCk
Assume that:

$\displaystyle y(x) = \arctan[ (5/3) (x^3 -1)]$

is a solution to your ODE, then so is:

$\displaystyle y(x) = \arctan[ (5/3) (x^3 -1)]+k$

for some constant $\displaystyle k$.

You have to choose $\displaystyle k$ so that the condition $\displaystyle y(1)=5 \pi$ is satisfied, and for that you need $\displaystyle k=5 \pi$.

So the solution to your ODE and condition is:

$\displaystyle y(x) = \arctan[(5/3) (x^3 -1)] + 5 \pi$

RonL

3. Hi all,

could someone post full working out please because i still can't get the answer. When i do it, i get c = tan(5*pi) -5/3

y = arctan( (5/3)x^3 + c)

Thanks,
ArTiCk