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Do Now: Finish yesterday’s sheet

Name: ____________________________ Date: _____________ AP Calculus AB: Separable Differential Equations Ms. Loughran Do Now:

1. sin xcos2 x

dx =∫

Differential equation: We can solve differential equations using a technique called separation of variables. You move different variables to opposite sides of the equation so that you can integrate both sides of the equation separately.

1. Solve for y if dydx

= (xy)2 and y = 1 when x = 1.

You can check by taking the derivative.

I Iff dx ftanxsecxdx.euto

an equationthatcontains a derivative

HiFIdy x'yDX

dff X dx

fy'dy fx2dx

yi Etc yEE Izuj I't

yx

I T toyt 4

4g c

y 7dad 3 I ftp.x.fff.FI

x'fixx'y Xy

24 321

I243125 14345

16 12 113 6

523712 2 3 1212

525 222 3212K2723

4 61211225361 423 32 3 2 273

Ifkdxt 5dx at2bt5xlat2bt5bFa 7b Ya

34THIpf6 3 Hya SHH

Homework 02-04

y 123 4874811

y 362 96 48

t t

36296 48 0

12132 8 41 0 3 2

12 3 211 2 0 CV CD cu yX X 2

lz.ge tcBehindthescenes u E

du Idt2dudt I 2eddie

Htc e tcEste

Las fsinks 32

3 6 13T

t to or tot

3 6 3 1 13

y E ask cos 1 0

y 2smally 2sin12ftIsin't20 2

y o 2Kft

f O t Oft 7Mmm Mmax

y x Yy 2x3

I taxFy taff f

m I

alwayst

O y 251 3try o y 5131 2

0 5 15213 511 151 2.6

8

dntdnt

2

2xt2ydd 0day 2

daffyH

txXdd

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3HHj311

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f x 170thatx'to

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f

fb H3 e te 2xfix e x 3 2x

f x e 1 22 3fix 1 4 3 1

D e x 3HttI