Question

Determine which of the following equations are separable. If it is separable, find its general solution. Then, match one of the differential equations to the slope field below and sketch the solution curve corresponding to an initial condition of y(0) = 0.
(i) y0 = y−2x

(ii) dy dx = −2x(y−3)

(iii) y00 + 4y = 6cos(t)

(iv)dy/dx=1/ y

Answer 1

Only (ii) and (iv) is separable differential equation.

ii>

integrating both side:

ln(y-3) = x^2 + C, where C is integral constant.

x = 0, y = 0

0 = 3 +k

=> k = -3

answer

Graph:

iv>>

integrating both side:

  

for x = 0, y = 0 => C = 0

therefore ,

answer

Graph :