So this isn't a homework problem persay, it was given information but I just couldn't wrap my head on why this was true.
We have 1-d heat transfer through a planar slab. If we have a T_a for the temperature outside, then as we T_1 for the temperature on one end of the surface, and T_2 for the...
Ah ok, I don't even need the general solution, just the particular solution, so should I just consider the two particular solutions of Asin(2x)+Bcos(2x) and y=1/4 (Solving the constants A and B?)
so (cos(x)^2) is ((1+cos (2x))/2.
Which is 1/2 + cos(2x)/2. Am I missing something to get it into a degree one term and a trig function?
For that I get A+ B*cos(2x)+C*sin(2x)?
Homework Statement
Find a particular solution yp of the differential equation
2y''+9y'+2y=(cos(x))^2
Homework Equations
The Attempt at a Solution
I'm not really sure where to start? I solve for the homogeneous solution and get C1e^ -4.26556+C2e^-.2344355629=0. I'm just not sure where to...
Yeah sorry, I was missing the first half of the question, if it says setup but don't solve for the coefficients for just the particular solution, is what I have correct because it keeps saying i'm wrong and I have no idea. Am I missing some steps?
Homework Statement
Set up but do not solve for the appropriate particular solution yp for the differential equation
y''+25y=2xsin(5x)
using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).
Homework Equations
The Attempt at a Solution
I first solved...
Eh it's online homework and it says "answer is incorrect" -.-"
I entered:
e^(-.5x)(a*cos(sqrt(3)*x/2)+bsin(sqrt(3)*x/2)) and my previewed answer was in the correct format too
Nope, it's given as a homogeneous equation (set equal to 0). Unless you're saying there's something i'm missing?
The full equation is y=e^(-.5x)(a*cos(*x/2)+bsin(*x/2))
Homework Statement
Question: I'm confused about how to app
Find the real-valued general solution of the differential equation
y''+1y'+1y=0
where primes indicate differentiation with respect to x. (Use the parameters a, b, etc., for undetermined constants in your solution.)
The...
Question:
Find the real-valued general solution of the differential equation
y''+1y'+1y=0
where primes indicate differentiation with respect to x. (Use the parameters a, b, etc., for undetermined constants in your solution.)
My attempt:
Use characteristic equation:
r^2+r+1=0
I used the...
Homework Statement
A wire lies along the piecewise linear curve extending from the point (4,3) to the point (6,15) to the point (12,15). If the density of the wire is given by (xy)=3xy+2y, use a line integral to find the mass of the wire.
Homework Equations
The Attempt at a Solution...
Homework Statement
Integrate the function f(xyz)=−4x+6y over the solid given by the figure below, if P = (5,1,0) and Q = (-5,1,5).
where P=(5,1,0) and Q=(-5,1,5)
Homework Equations
r²=x²+y²
tan theta=y/x
z=z
y=rsintheta
x=rcostheta
The Attempt at a Solution
So I treated this...
Homework Statement
Integrate the function f(xyz)=−4x+6y over the solid given by the "slice" of an ice-cream cone in the first octant bounded by the planes x=0 and y=x*sqrt(22/3) and contained in a sphere centered at the origin with radius 13 and a cone opening upwards from the origin with top...