How to solve the differential equation (dy/dx)^2 - 3(dy/dx) = -2

Heya,

I'm stuck on this question, I have no idea how to approach this question with the (dy/dx)^2, any help appreciated,

cheers :)

Put z = dy/dx

z² - 3z + 2 = 0

=> z = dy/dx = 1 or 2

=> y = x + c1 or 2x + c2

Use method of undetermined coefficients:

y'' - 3y' = -2

First solve for the homogeneous D.E where y'' - 3y' = 0.

y = e^(rx)

r^2 - 3r = 0

r = 0 and r = 3

y = C_1 + C_2*e^(3x)

We seek a particular solution of the form y_p = Ax

(y_p)' = A

(y_p)'' = 0

-3A = -2 --> A = 2/3

So the general solution is: y = C_1 + C_2*e^(3x) + 2x/3