Recent content by popopopd

if we do picard's iteration of nth order linear ODE in the vector form, we can show that nth order linear ODE's solution exists. (5) (17) example) (21) (22) (http://ghebook.blogspot.ca/2011/10/differential-equation.html)I found that without n number of initial conditions, the solution...

(5) (17) - using picard's iteration in vector form, to prove nth order linear ODE's existence & uniqueness. ex (21) (22) (http://ghebook.blogspot.ca/2011/10/differential-equation.html)Hi, I actually did picard's iteration and found that...

Thanks! it helped alot!

hi, I looked up the existence and uniqueness of nth order linear ode and I grasped the idea of them, but still kind of confused why we get n numbers of general solutions.

for example, y_g= ay1(x0)+by2(x0)+cy3(x0) ... nyn(x0)=y0 , cy3(x0)=y0 and the rest are 0 y_g'=ay1'(x0)+by2'(x0)+cy3(x0)' ... nyn(x0)=y'0, by3(x0)=y'0 and the rest are 0 and so on

hi, could you explain me why nth order linear ode must have n number of general solutions?is it because we are given with n number of initial conditions to find the general solution, and if so,y_g= ay1(x0)+by2(x0)+cy3(x0) ... nyn(x0)=y0 y_g'=ay1'(x0)+by2'(x0)+cy3(x0)' ... nyn(x0)=y'0 ... and in...

yeah thanks, they did. I think they are wrong.

Ah I found it. by definition wavenumber is v/c and that gave the equation 'c'

hi, i am a lillte confused why the equation for hookes law is 1/(2pi*c)*sqrt(k/m_reduced)? where does c come from? http://www.massey.ac.nz/~gjrowlan/intro/lecture5.pdf - slide 8. also, is there any particular reason why we use reduced mass?

isn't it 3(a+b)+4? I really appreciate you for explanation. so, y1 and y2 general solutions are algebraic so they can form a vector space (when homogeneous since it needs to pass through origin), and particular answer is thought to be translation with respect to the given origin by function...

hmm, I am a little confused at this part of Linear ODE. general solution can be found when the equation is y''+ p(x)y'+ y= 0. so I understood this way. y''+ p(x)y'+ y= f(x), and if f(x)=0 for some x, then y''+ p(x)y'+ y= 0 is included in the non-homo 2nd linear ode. so y''+ p(x)y'+ y= 0 is...

2nd order ODE has a form y''+p(x)y'+q(x)y=f(x)and if we assume f(x)=/=0 for every x, then y''+p(x)y'+q(x)y=/=0 so in this case we can't specify general solution of 2nd order ode?