the solution technique is easy but I'm exhausted and having surgery...by the way what is the partial fraction expansion for this differential equation? thanks very much!

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- April 22nd 2013, 07:06 PMmathlover10ODE Integral by partial fractions
the solution technique is easy but I'm exhausted and having surgery...by the way what is the partial fraction expansion for this differential equation? thanks very much!

- April 22nd 2013, 08:57 PMmathguy25Re: ODE Integral by partial fractions

Multiply both sides by

Therefore,

Then and so then . Then so . Then . Thus, .

Note that . Then . Then i.e. . Then . This implies that and .

Thus, and .

Thus,

Now, apply direct u-substitute on each summand. - April 22nd 2013, 09:28 PMmathlover10Re: ODE Integral by partial fractions
oh right, so for example in the situation that Q(x) has irreducible quadratic factors none of which is repeated...

- April 23rd 2013, 02:34 AMProve ItRe: ODE Integral by partial fractions
- April 23rd 2013, 09:45 PMmathlover10Re: ODE Integral by partial fractions
thanks very much! so when you do the partial fraction expansion the 2nd term has 4 terms in the numerator because it is t^4? is it more correct to express it in this form with a constant added to the integral? sometimes the coefficient system can also be represented by a matrix and solved by Gaussian elimination