Question

Could someone tell me the steps of solving this 2nd order differential equation?

(x^2)y'' - x y' + y = 8(x^3)

Is it Euler's equations for the left side and method of undertermined coeffficients for the right side? Thanks!!!

Answer 1

yeah or you can use vartiation of parameters

Answer 2

thanks but how do you solve for the left side of the equation which now looks: y'' - (1/x) y' + y/(xsquared) = 8x

Answer 3

you leave the left side as it is and solve for the characteristic equation using cauchy eulers

Answer 4

and i would use variation of parametesr after because i actually don't think undetermined coefficients work

Answer 5

so apply euler right off the bat to the left side which is : y'' - 2y' + y = 0
and use variation of parameters to get the particular solution?

Answer 6

yes but when you apply variation of parameters remember to get a coefficient of 1 on y'' so that your g(t)=x

Answer 7

what do you mean by getting a coefficient of 1 on y''?

Answer 8

because the form to use variation of parameters is y''+q(t)y'+p(t)y=g(t)

Answer 9

yeahh my bad...thanks a lot

Answer 10

Could you verbally tell me the steps of solving this system of differential equations as well? Thanks!!!

x'= x-y+z
y'= x+y-z
z'= 2x-y

Answer 11

you take the laplace of each equation and then cancel to try to get X Y or Z by itself and then inverse laplace that to solve for that and plug back in to solve for other two.. it's an algebraic nightmare so i suggest you use wolfram to help simplify things :P

Answer 12

Okok thanks at least i know how to attack it now. Thanks a lot. Do you engineers use DE everyday?

Answer 13

DE is probably one of the most useful maths compared to the other ones. But technically I haven't even taken my DE course yet, I just learned it on my own right now. I have it next semester, so I can plan on skipping class :P. And it does show up quite a bit in engineering, though in real life, most DE are most likely solved by a computer. It is still crucial to understand how they work and the meaning behind them though

Answer 14

what method is that nikvist? i've never seen that method before =o

Answer 15

this is the product rule

Answer 16

why is y = xz?

Answer 17

this is substitution \[y(x)=x\cdot z(x)\]

Answer 18

replace x=0 in starting differential equation, you will get y=0
\[\Rightarrow\quad y(x)=x\cdot z(x)\]

Answer 19

thanks a lot! do you know how to use power series here instead?

Answer 20

yeah i know product rule is involved but isnt there a name for the method?

Answer 21

spacenight: what he did is called "reduction of order" but in order to do that we needed to know 1 of the 2 solutions. He just assumed y1(x) = x here.

Answer 22

so i don't think he started off the right way

Answer 23

http://www.physicsforums.com/showthread.php?t=151779

Answer 24

lol oh yeah i know reduction of order, i just didnt know why y=xz is an assumed solution.. hm that's weird, i'd prefer to just do it the other way, that's how it was done in our homework for us