solve: dy/dx= COS(x+y+1)

Question

dy/dx=COS(x+y+1)

Answer 1

Let y(x)+x+1 → Ø(x)

Answer 2

Y'(x)= Ø'(x)-1

Answer 3

The given is transformed in to:

Answer 4

dø/dx=1+COSØ

Answer 5

So we have

Answer 6

{dø/1+COSØ={ dx

Answer 7

Now we use the Z- transform for the left integrand:

Answer 8

e^iø =Z

Answer 9

dø=dz/iz

Answer 10

And1+COSØ_=1+z^2 +1/2z

Answer 11

Z^2+2Z+1/2Z

Answer 12

=(z+1)^2 /2z

Answer 13

{dø/1+cosø →"z base "

Answer 14

{2z/(z+1)^2 • dz/iz=2/i

Answer 15

{ d(z+1) /(z+1)^2=2i/z+1

Answer 16

That is,

Answer 17

{ dø/1+cosø=2i/1+e^iø

Answer 18

Now 2i/1+e^iø=x+c

Answer 19

→1+e^iø

Answer 20

=2i/x+c

Answer 21

→ e^iø=2i/x+c -1

Answer 22

iø= ln(2i/x+c -1)

Answer 23

→ ø= i ln{x+c/2i-(x+c)}

Answer 24

Y=ø-(x+1)

Answer 25

Y=-(x+1)+i ln{x+c/2i-(x+c)}

Answer 26

I want to continue the answer of this question:

Answer 27

{ dø/1+COSØ

Answer 28

= 2i/1+cisø

Answer 29

=2i•cis(-ø/2)/cis(ø/2)+cis(-ø/2)

Answer 30

=i•cis(-ø/2)/COS(ø/2)

Answer 31

=1/COS(ø/2) •i [COS ø/2-iSIN ø/2]

Answer 32

=TAN ø/2+i

Answer 33

Therefore,TAN(ø/2)+i

Answer 34

= x + c power ~

Answer 35

→ TAN(ø/2)

Answer 36

=x + c

Answer 37

Ø= x+y+1 ,

Answer 38

Y+x+1=2 ARTAN(X+C)