Separating variables, we have
![\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cdfrac%20xy%20%5Cimplies%20y%5C%2Cdy%20%3D%20x%5C%2Cdx)
Integrate both sides.
![\displaystyle \int y\,dy = \int x\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20y%5C%2Cdy%20%3D%20%5Cint%20x%5C%2Cdx)
![\dfrac12 y^2 = \dfrac12 x^2 + C](https://tex.z-dn.net/?f=%5Cdfrac12%20y%5E2%20%3D%20%5Cdfrac12%20x%5E2%20%2B%20C)
Given that
, we find
![\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12](https://tex.z-dn.net/?f=%5Cdfrac12%20%28-1%29%5E2%20%3D%20%5Cdfrac12%200%5E2%20%2B%20C%20%5Cimplies%20C%20%3D%20%5Cdfrac12)
Then the particular solution is
![\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12](https://tex.z-dn.net/?f=%5Cdfrac12%20y%5E2%20%3D%20%5Cdfrac12%20x%5E2%20%2B%20%5Cdfrac12)
![y^2 = x^2 + 1](https://tex.z-dn.net/?f=y%5E2%20%3D%20x%5E2%20%2B%201)
![y = \pm\sqrt{x^2 + 1}](https://tex.z-dn.net/?f=y%20%3D%20%5Cpm%5Csqrt%7Bx%5E2%20%2B%201%7D)
and because
, we take the negative solution to accommodate this initial value.
![\boxed{y(x) = -\sqrt{x^2+1}}](https://tex.z-dn.net/?f=%5Cboxed%7By%28x%29%20%3D%20-%5Csqrt%7Bx%5E2%2B1%7D%7D)
Answer:
the answer is 20
Step-by-step explanation:
180+180=360
80+70=150
180-150=20
Answer:
12???
Step-by-step explanation:
3.30 x 5 = 16.50
4.30 x 7 = 30.10
30.10 + 16.50 = $46.60
Answer:
see below
Step-by-step explanation:
Find the magnitude (-1)^2 + (sqrt3)^2 = m^2 m = 2
find the angle arctan (sqrt3/-1) = 120 degrees
the cube root would then be
(cos 40 + isin 40)