de-t2-a(1)

3(15 pts find a particular integral y p of the

Info iconThis preview shows pages 2–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ______________________________________________________________________ 3. (15 pts.) Find a particular integral, y p , of the differential equation Obviously the driving function here is NOT a UC function. Thus, we must use variation of parameters to nab the culprit. Corresponding Homogeneous: F.S. = {sin(2 x ), cos(2 x )}. If y p = v 1 cos(2 x ) + v 2 sin(2 x ), then v 1 ′ and v 2 ′ are solutions to the following system: Solving the system yields v 1 ′ = -2 and v 2 ′ = 2cot(2 x ). Thus, by integrating, we obtain Thus, a particular integral of the ODE above is ______________________________________________________________________ 4. (10 pts.) Set up the correct linear combination of undetermined coefficient functions you would use to find a particular integral, y p , of the O.D.E. First, the corresponding homogeneous equation is which has an auxiliary equation given by 0 = m 2- 6 m + 10. Thus, m = 3 + i or m = 3 - i , and a fundamental set of solutions for the corresponding homogeneous equation is { exp(3 x )cos( x ), exp(3 x )sin( x ) }. Taking this into account, we may now write ______________________________________________________________________ Bonus Noise: If , then the first n derivatives are nonzero and given by Higher order derivatives are zero. If f is a solution to (*) where m > n , then by direct substitution (**) The left side of (**) is a nonzero polynomial of degree at most n if there is some a k nonzero for some k with 0 ≤ k ≤ n . Such a polynomial has at most n roots. So in this case, we would not have a function identity on anymost n roots....
View Full Document

{[ snackBarMessage ]}

Page2 / 4

3(15 pts Find a particular integral y p of the differential...

This preview shows document pages 2 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online