Answer:
![(x + 2x^2)-\frac{1}{18}\ln |15+18y|=C'](https://tex.z-dn.net/?f=%28x%20%2B%202x%5E2%29-%5Cfrac%7B1%7D%7B18%7D%5Cln%20%7C15%2B18y%7C%3DC%27)
Step-by-step explanation:
Given differential equation,
![\frac{dy}{dx}=15+30x+18y + 36xy](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D15%2B30x%2B18y%20%2B%2036xy)
![\frac{dy}{dx}=15(1+2x)+18y(1+2x)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D15%281%2B2x%29%2B18y%281%2B2x%29)
![\frac{dy}{dx}=(15+18y)(1+2x)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%2815%2B18y%29%281%2B2x%29)
![\frac{dy}{15+18y}=(1+2x)dx------(1)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7B15%2B18y%7D%3D%281%2B2x%29dx------%281%29)
Let 15 + 18y = t
18dy = dt
![\implies dy=\frac{dt}{18}](https://tex.z-dn.net/?f=%5Cimplies%20dy%3D%5Cfrac%7Bdt%7D%7B18%7D)
From equation (1),
![\frac{1}{18} \frac{1}{t}dt = (1+2x)dx](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B18%7D%20%5Cfrac%7B1%7D%7Bt%7Ddt%20%3D%20%281%2B2x%29dx)
Integrating both sides,
![\frac{1}{18}\ln |t| = x + 2x^2 + C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B18%7D%5Cln%20%7Ct%7C%20%3D%20x%20%2B%202x%5E2%20%2B%20C)
![\frac{1}{18}\ln |15+18y| = x + 2x^2 + C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B18%7D%5Cln%20%7C15%2B18y%7C%20%3D%20x%20%2B%202x%5E2%20%2B%20C)
( where C' = -C = constant)
Which is the required equation,
Where,
![G(x) = x+2x^2\text{ and }H(y) = -\frac{1}{18}\ln |15+18y|](https://tex.z-dn.net/?f=G%28x%29%20%3D%20x%2B2x%5E2%5Ctext%7B%20and%20%7DH%28y%29%20%3D%20-%5Cfrac%7B1%7D%7B18%7D%5Cln%20%7C15%2B18y%7C)
Answer:
720 ways
If you've got six cards you can arrange them in 6! ways = 720 ways.
Step-by-step explanation:
thank me later
Subject: dolphin
verb: swam
adjectives: young
prepositional phrase: i think is near
Compare the given equation with the general equation of a circle
Given equation: x² + y² - 8x +6y +9 = 0
Equation of a circle: x² + y² + 2gx + 2fy + c = 0
2g= -8; g = -8÷2= -4
2f = 6; f = 6÷2 = 3
c= 9
Solving for radius of the circle...
r =√g² + f² - c
g= -4, g² = ±16
f = 3, f² = 9
Substituting, we have
r = √16 + 9 - 9
r = √25-9
r=√16
r = 4
Therefore, the centre and radius of the circle is 9 and 4 respectively.
Hope this helped!
Please mark brainliest;-)
The value of the expression is 4