Help With Diff Equations & Vectors????

Question

1) Solve the differential equation

dy/dx = -3x^2 + 3x + 2 + (2/x)y

2) Solve the linear differential equation

dy/dx = (4 - (x + 2)y) / (x + 1) , y(0) = 7

3) Find the scalar and vector projections of b onto a, where

b = - i - 4j + k and a = 3i + 7j + 5k

a) (scalar projection) compab =

b) (vector projection) projab =

Answer 1

For prob 1:

- factor out the y by multiplying 1/y to bothsides and multiplying dx to bothsides. So u get something like this

   dy/y = [-3x^2 + 3x + 2 + 2/x ]dx

- Then you integrate both sides.

   Ln y = -x^3 + 3/2x^2 + 2x + 2*integral of dx/x . So this equals

   Ln y = -x^3 + 3/2x^2 + 2x + 2*lnx + C

- Then you take the exponential to take out the Ln in Y to make it into an equation.

   e^ln y = Y

So then you do the same for the right side and you got yourself an equation. Hope this helps. Again, im not sure on my calc rite now, i forgot everything, lol. But i think it should go something like i wrote.