Find the particular solution to y ' = 2sin(x) given the general solution is y = C − 2cos(x) and the initial condition y of pi over 2 equals 1.

Question

anonymous · Answer

https://i.gyazo.com/f13d3491671ec01918216aea0512c459.png

irishboy123 · Answer

what do you think??

it all seems to be included in the info pack.....

anonymous · Answer

What info pack?

irishboy123 · Answer

you have the DE and the solution.  

what is there left to do apart from plug and play!!

anonymous · Answer

Can you show me how it's done? I have about 3 more of the same question and I'm not really sure how to approach it. What do I plug and why?

freckles · Answer

you have the condition y(pi/2)=1
this says when x=pi/2 we have y=1
plug into your solution to find C

freckles · Answer

do you see your solution is y=C-2cos(x) right?
Find the constant C using the point (x=pi/2,y=1)
replace x with pi/2 
replace y with 1
solve for C
you can do this! :)

anonymous · Answer

C=1
Final answer is C?

freckles · Answer

$$y=C-2 \cos(x) \ 1=C-2 \cdot \cos(\frac{\pi}{2}) \ 1=C-2(0) \1=C  \ \text{ yes you should have } \ y=1-2\cos(x)$$