Differential equationsRandomize Question code: 1a923A Question 1001 The variables x{x}x and y{y}y satisfy the differential equation 3dydx=9−2y.3 \frac{\mathrm{d}y}{\mathrm{d}x} = 9 - 2 y.3dxdy=9−2y. (i) Find y{y}y in terms of x,{x,}x, given that y=5{y = 5}y=5 when x=0.{x = 0.}x=0. (ii) State what happens to y{y}y for large values of x.{x.}x. Answer (i) y=92+12e−23x.{y = \frac{9}{2} + \frac{1}{2} \mathrm{e}^{- \frac{2}{3} x}.}y=29+21e−32x. (ii) y→92.{y \to \frac{9}{2}.}y→29. Randomize Question code: 1a923A
The variables x{x}x and y{y}y satisfy the differential equation 3dydx=9−2y.3 \frac{\mathrm{d}y}{\mathrm{d}x} = 9 - 2 y.3dxdy=9−2y. (i) Find y{y}y in terms of x,{x,}x, given that y=5{y = 5}y=5 when x=0.{x = 0.}x=0. (ii) State what happens to y{y}y for large values of x.{x.}x.
(i) y=92+12e−23x.{y = \frac{9}{2} + \frac{1}{2} \mathrm{e}^{- \frac{2}{3} x}.}y=29+21e−32x. (ii) y→92.{y \to \frac{9}{2}.}y→29.