At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
yeah or you can use vartiation of parameters
thanks but how do you solve for the left side of the equation which now looks: y'' - (1/x) y' + y/(xsquared) = 8x
you leave the left side as it is and solve for the characteristic equation using cauchy eulers
and i would use variation of parametesr after because i actually don't think undetermined coefficients work
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?
yes but when you apply variation of parameters remember to get a coefficient of 1 on y'' so that your g(t)=x
what do you mean by getting a coefficient of 1 on y''?
because the form to use variation of parameters is y''+q(t)y'+p(t)y=g(t)
yeahh my bad...thanks a lot
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
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
Okok thanks at least i know how to attack it now. Thanks a lot. Do you engineers use DE everyday?
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
what method is that nikvist? i've never seen that method before =o
this is the product rule
why is y = xz?
this is substitution \[y(x)=x\cdot z(x)\]
replace x=0 in starting differential equation, you will get y=0 \[\Rightarrow\quad y(x)=x\cdot z(x)\]
thanks a lot! do you know how to use power series here instead?
yeah i know product rule is involved but isnt there a name for the method?
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.
so i don't think he started off the right way
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