Recent content by kape

Thank you for you detailed answer! But I am still a little confused about the part where you change the index for y'.. why did you change the index for y'? Since it is 6xy' wouldn't I have to do add another x to the the series? So that it becomes: y' =...

y''-6xy'+(6x^2-2)y=0 y_{1} = _____________ I have to solve the above equation using power series.. but I am stuck. What I have so far is: y=\sum_{m=0}^\infty a_{m}x^{m} y'=\sum_{m=1}^\infty ma_{m}x^{m-1} y''=\sum_{m=2}^\infty m(m-1)a_{m}x^{m-2} = \sum_{m=0}^\infty...

Very sorry, but I just don't know.. If there is a 5kg load on an object, let's say a book on a table.. what is it's force in kgN? Is it 5kg x 9.8?!

I've also tried checking some of the calculations using Matlab and they seem to be correct.. I get the feeling that it's not the calculation but the method? Also, I've managed to find info on factorizing.. I found out there was this thing called the Factor Theorem and Long Division!

Nonhomogenous LODE (Higher Order) - Method of Variation of Parameters x^3y''' + x^2y'' - 2xy' + 2y = x^3log(x) y(1) = \frac{10}{32} y'(1) = -\frac{24}{32} y''(1) = -\frac{11}{16} I know that \inline y = y_h + y_p and that I probably should use the method of variation...

Higher Order Homogenous ODE (Euler-Cauchy) *sigh* I am (yet again) stuck on a problem.. I would greatly appreciate any help! x^3y''' - 3x^2y'' + (6-x^2)xy' - (6-x^2)y = 0 \inline y_1 = x is a solution to the equation above y'(0) = 3 y''(0) = 9 y'''(0) = 18 I'm not quite sure...

Oh I see.. four distinct roots! Thank you. I managed to solve the problem without any difficulties! I guess I was muddled with the definitions of roots... I've been looking through my textbook but I'm still not exactly sure of the definitions.. ----------------- Am I right to think...

Hello, I have two questions about this problem: (D^4 + 5D^2 + 4)y = 0 y(0) = 10 y'(0) = 10 y''(0) = 6 y'''(0) = 8 \lambda^4 - 5\lambda^2 + 4 = 0 (\lambda^2 + 4) (\lambda^2 + 1) Until here I am fairly sure that I didn't mess it up.. But I'm not sure if I have the roots...

oh! thank you! i just understood! :D

Higher Order Homogeneous ODE (IVP) [Solved] I am having problems with this IVP: y'''' + y' = 0 y(0) = 5 y'(0) = 2 y''(0) = 4 What I have done so far is: \lambda^3 + \lambda = 0 \lambda(\lambda^2 + 1) = 0 So one roots is \lambda = 0 (though.. can there be a root that...

I have a few nagging questions that are preventing me from solving calculus problems.. Can someone give me a hand? ---------- Question 1 e^xy' = (4x+1)y^2 From the equation above, is it possible to do this: \frac{y'}{y^2} = \frac{4x+1}{e^x} Aren't you supposed to divide one...

Oh! But... doesn't a quadratic equation have to be in the form ax^2 + bx + c = 0; doesn't it have to equal zero? How do I do it if it equals 8x? Could you tell me about the 6C = C bit from the previous equation? I'm running into a lot of equations where I have to multiply a constant, and...

I also encountered something new and I'm not sure what to do: The problem is: y' = \frac{1-7y-49x}{1+y+7x} with \inline y^2(1)=7 using \inline (y + 7x = v) I've managed this so far: v'-7 = \frac{1-7v}{1+v} v' = \frac{-7(1+v)}{1+v} + \frac{8}{1+v} + 7...

Thank you for answering questions 1 & 2.. I think I understand. Sorry question 3 was deleted, don't quite know how that happened. Also, I have one more question: (which is kind of similar to question 3) ---------- Question 6 How do you integrate: \int \frac{1}{x^a} dx...

No, no, no! Though I am fairly sarcastic at times, I assure you I was NOT sarcastic this time! I realize that I did overdo it a little bit, but I really was overwhelmed with joy! You don't know how happy I was to be liberated from hours of frustration... and to be able to solve a question in...