# Math Help - 2nd order DE

1. ## 2nd order DE

Y''+Y'+Y = e^3x + cos(5x)

how to solve this DE??? Great Help

2. Originally Posted by scifreak
Y''+Y'+Y = e^3x + cos(5x)

how to solve this DE??? Great Help
Step 1: Can you solve Y'' + Y' + Y = 0? Please show all your work and say where you're stuck if you can't solve it.

3. i solved it upto Y"+Y'+Y= 0. it can be solved using the general second order DE solution steps. But the problem is the Right hand side of the equation. How to solve that part? I mean how to find the Particular Integral ..... The answer for the first part of is

Yc=e^(-0.5x) (Acos(root(3)/2) + B sin (root(3)/2) )

my problem again is as to how to find the Particular integral

4. Originally Posted by scifreak
i solved it upto Y"+Y'+Y= 0. it can be solved using the general second order DE solution steps. But the problem is the Right hand side of the equation. How to solve that part? I mean how to find the Particular Integral ..... The answer for the first part of is

Yc=e^(-0.5x) (Acos(root(3)/2) + B sin (root(3)/2) )

my problem again is as to how to find the Particular integral
Use the method of undetermined coefficients to find a particular solution of the form $y = a e^{3x} + b \cos (5x) + c \sin (5x)$.

5. Thank you sir, Problem solved. I will solve it and if i have further problems i will notify you