Homework Statement
If d^2/dx^2 + ln(x)y = 0[/B]
Homework Equations
included in attempt
The Attempt at a Solution
I was confused as to whether I include the power series for ln(x) in the solution. It makes comparing coefficients very nasty though.
Whenever I expand for m=0 for the a0 I...
Homework Statement
Given a set of fundamental solutions {ex*sinx*cosx, ex*cos(2x)}
Homework Equations
y''+p(x)y'+q(x)=0
det W(y1,y2) =Ce-∫p(x)dx
The Attempt at a Solution
I took the determinant of the matrix to get
e2x[cos(2x)cosxsinx-2sin(2x)sinxcosx-cos(2x)sinxcosx-...
Homework Statement
Solve y''+(cosx)y=0 with power series (centered at 0)
Homework Equations
y(x) = Σ anxn
The Attempt at a Solution
I would just like for someone to check my work:
I first computed (cosx)y like this:
(cosx)y = (1-x2/2!+x4/4!+ ...)*(a0+a1x+a2x2 +...)...
Homework Statement
imgur link: http://i.imgur.com/Bv3qtPm.png
Homework Equations
The Attempt at a Solution
From the FBD it is apparent that there is a constraint
-k_1x_1 + k_2(x_2-x_1) + 5\cos{10t} = 0
If you combine this with
{x}''_1 = -(k_1+k_2)x_1 + k_2x_2 + 5\cos{10t}
and...
I know how to solve \frac{d\vec{u}}{dt} = A\vec{u}, I was just watching a lecture, and the lecturer related that solving that equation is pretty much a direct analogy to \vec{u} = e^{At}\vec{u}(0), in so far as all we need to do after that is understand exactly what it means to take the...
Homework Statement
I am attempting to understand this example shown below:
Homework Equations
During stead state DC, the capacitor is an open circuit and the inductor is short circuited.
The Attempt at a Solution
[/B]
The questions I have are really related to the concepts as I don't...
Homework Statement
Well I am looking for the particular integral of:
d2y/dt2 + 4y = 5sin2t
The attempt at a solution
As f(t) = 5sin2t, the particular integral yPI should look like:
yPI = Acos2t + Bsin2t
dyPI/dt = -2Asin2t + 2Bcos2t
d2yPI/dt2 = -4Acos2t - 4Bsin2t
Subbing in to the differential...
Homework Statement
Regarding the case where the auxillary (characteristic) equation has complex roots, we solve the quadratic in the usual way using i to get the general solution
y(x) = e^{\alpha x}\left(C_1 \cos{\beta x} + i C_2 \sin{\beta x}\right)
And the textbook shows
y(x) = e^{\alpha...