# Differential Equations

• February 16th 2009, 08:10 AM
mr_motivator
Differential Equations
a) Write down the general solution to the differential equation dy/dx + 5y = 0.

b) Use a suitable trial function to find one simple particular solution of dy/dx + 5y = 3e^(-9x)

c) Find the solution of dy/dx + 5y = 3e^(-9x) that satisfies y(0) = -27/4.

Cheers...
• February 16th 2009, 08:25 AM
Moo
Quote:

Originally Posted by mr_motivator
a) Write down the general solution to the differential equation dy/dx + 5y = 0.

What, you can't do that ? o.O

$\frac{dy}{dx}=-5y$
$\frac{dy}{y}=-5 ~dx$
The LHS integrates to $\ln(y)$, the RHS integrates to $-5x+c$

Quote:

b) Use a suitable trial function to find one simple particular solution of dy/dx + 5y = 3e^(-9x)
Try something like $k e^{-9x}$...

Quote:

c) Find the solution of dy/dx + 5y = 3e^(-9x) that satisfies y(0) = -27/4.

Cheers...
Use the above.