Question

@Mathematics Hi,can someone help me with this differential equation: y''''-3y'''+2y''=2x+e^x*sinx
how to solve it?

Answer 1

what is being asked?

Answer 2

I even dont know how to start solving it.

Answer 3

i think the fifth derivative?

Answer 4

fourth

Answer 5

LOL the fourth is just algebra....

Answer 6

first you find the characteristic polynomial, if that's what it is called in English.

Answer 7

what i have to do after characteristic polynomial?

Answer 8

if you want the outline of a method it's this

1. First recognize this is actually a second order linear inhomogeneous equation. Write u = y'' and you have a 2nd order equation in u(x)

2. Now to solve such an equation you need to
2a. Find the homogeneous solutions
2b. Find the particular/inhomogeneous solutions
2c. Write down the general solution as the the some of the homogeneous and inhomogeneous solutions

If the steps 2a-c are mysterious, watch some lectures beginning here:
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-9-solving-second-order-linear-odes-with-constant-coefficients/

Answer 9

oh my god?

Answer 10

Oh, and step 3: now integrate the general solution for u(x) to find y(x)

Answer 11

What's "oh my god?"

Answer 12

There's no simpler method for tackling this kind of problem than what James recommended.

I'd suggest you make good use of what the MIT/OCW project above has to offer regarding this subject. ^^

Answer 13

Thanks.

Answer 14

Could Laplace transform maybe be used as a simpler method to solving this?

Answer 15

I don't think a Laplace transform is an easier method! But even in theoretical terms, if you don't understand the basic solution method, a Laplace transform isn't going to help you. In any case, you don't need the Laplace method here.

Answer 16

I understand, but I was just asking. I was just wondering if I would get the same result. I heard somewhere that the Laplace transform has some limitations to solving diff. equations, so I was just wondering

Answer 17

We would definitely get the same result, with the twist of having to introduce dummy initial conditions for the ODE in the Laplace method case.

Answer 18

Ok, thank you...