Question

Find the particular solution of the equation which y = 1 when x = 0, and then give this particular solution in explicit form.

Answer 1

\[36y= (\exp ^{(-3x+2sinx)/6})^{6}\]

Answer 2

\[36y=\left( e^{\frac{-3x+2\sin x}{6}}\right) ^6=e^{{-3x+2\sin x}}\]

Answer 3

Yes.

Answer 4

a good first first i would think

Answer 5

step*

Answer 6

Can you run through how you got that result?

Answer 7

\[\left(e^{\frac{-3x +2\sin x}{6}}\right)^6\]\[=\left(e^{\frac{-3x +2\sin x}{6}}\right)\left(e^{\frac{-3x +2\sin x}{6}}\right)\left(e^{\frac{-3x +2\sin x}{6}}\right)\left(e^{\frac{-3x +2\sin x}{6}}\right)\left(e^{\frac{-3x +2\sin x}{6}}\right)\left(e^{\frac{-3x +2\sin x}{6}}\right)\]\[=\left(e^{6\left(\frac{-3x +2\sin x}{6}\right)}\right)\]\[=\left(e^{-3x +2\sin x}\right)\]

Answer 8

It is already integrated.

Answer 9

i dont really understand the question

Answer 10

shouldn't there be a constant /

Answer 11

Ohhhh! Yes it should be +C in the right hand side within bracket. Sorry!

Answer 12

\[36y= (\exp ^{(-3x+2sinx)/6} +C)^{6}\]

Answer 13

how did i know that?
because we are solving for c such that
y = 1 when x = 0
this was impossible before
as 36≠1]

Answer 14

\[36y=\left(e^\frac{(−3x+2 \sin x)}{6}+C\right)^6\]

Answer 15

Yes

Answer 16

when y=1, x=0
\[36y=\left(e^\frac{(-3(0)-2sin0)}{6}+C\right)^6\]\[36=\left( e^0+C \right) ^6\]\[36=\left( 1+C \right) ^6\]

Answer 17

\[\sqrt[6]{36}=1+C\]

Answer 18

\[C=\sqrt[6]{36}-1\]\[=36^{1/6}-1\]

Answer 19

Great.

Answer 20

\[=(6^2)^{1/6}\]\[=6^{1/3}=\sqrt[3]{6}\]

Answer 21

so \[C=\sqrt[3]{6}-1\]

Answer 22

3rd root. Can see very well

Answer 23

Can't see very well small print. I assume it is

Answer 24

many thanks to you.

Answer 25

\[{\large C=\sqrt[3]{6}-1=6^{\left(\frac 1 3\right)} -1}\]

Answer 26

\[\frac{dy}{dx}= (2 \cos x − 3) e^{(−3x+2 \sin x)/6} y^{5/6}?\]

Answer 27

Yes

Answer 28

what is the y^5/6 thing doing?

Answer 29

*y^5/6 after expo

Answer 30

it is just timesed on is it?

Answer 31

part 1 (2cos) . part 2 (exp). part3 (y^)

Answer 32

Hope that is clear

Answer 33

it is clear now