Set up the appropriate form of the particular solution to each
of the differential equations below,...
Set up the appropriate form of the particular solution to each
of the differential equations below, but do NOT determine the
values of the coefficients.
Determine the form of a particular solution to the following
differential equations (do not evaluate coefficients).
(a)y′′ −4y′ = x+1+ xe^(2x) + e^(4x) + e^(4x)sin4x
1. Determine the form of a particular solution for the following
differential equations. (Do not evaluate the coefficients.)
(a) y'' − y' − 6y = x^2 e^x sin x + (2x^3 − 1)e ^ cos x.
(b) y'' − y' − 6y = (2 − 3x^3 )e^3x .
(c) y'' + 4y' + 4y = x(e^x + e^−x )^2 .
(d) y'' − 2y' + 2y = (x − 1)e^x sin x + x^2 e^−x cos x.
2. Find a...
For each of the following differential equations, find the
particular solution that satisfies the additional given property
(called an initial condition).
y'y = x + 1
Determine the reasonable form of the particular solution for
each non homogeneous differential equation. Do not solve it.
a) y''-y'-2y= e^-x+xcos2x+e^xsin2x.
b) D^2[y] +4y =1+x^2+xsin2x.
Find the general solution of the following
differential equations (complementary function
+ particular solution). Find the particular solution by inspection
or by (6.18), (6.23),
or (6.24). Also find a computer solution and reconcile differences
if necessary, noticing
especially whether the particular solution is in simplest form [see
(6.26) and the discussion
after (6.15)].
(D2+2D+17)y = 60e−4x sin 5x
Using variation of parameters, find a particular solution of the
given differential equations:
a.) 2y" + 3y' - 2y = 25e-2t (answer should be: y(t) =
2e-2t (2e5/2 t - 5t - 2)
b.) y" - 2y' + 2y = 6 (answer should be: y = 3 + (-3cos(t) +
3sin(t))et )
Please show work!
The SIR Model for the Spread of Disease
Set up the three differential equations and perform a simulation
of the solution of the three equations. Start with a Susceptible
(S) of 327,500,000 (the population of the US) and I value of 1 and
an R value of zero. Derive your constants, r,a so your simulation
matches current values of I and R. Use a dt of 1 day.
1.
Set-up the appropriate differential equation(s) and solve to
derive the general equation of motion for a human sized “dummy”
moving vertically (up/down) under the following assumptions:
(a)The initial elevation is h0 ft.
(b)The initial velocity is V0 ft./sec.
(c)All motion vertical (ignore any sideways motion).
(d)The force due to wind is proportional to velocity and in the
opposite
direction of velocity.
(e)The “terminal velocity” is 120mph (e.g. lim
t→∞ (V)= 120 mph).
(f)Force = Mass * Acceleration.
(g)Acceleration due to...
Solve each system. Express the solution set using vectors.
Identify a particular solution and the solution set of the
homogeneous system.
(a) 3x + 6y = 18
x + 2y = 6
(b) x + y = 1
x − y = −1
(c) x1 + x3= 4
x1 − x2 + 2x3 = 5
4x1 − x2 + 5x3 = 17
(d) 2a + b − c = 2
2a + c = 3
a − b = 0...
Write down Maxwell’s equations in differential and integral form
and explain the physics behind each one of them. Modify one of them
to account for the existence of magnetic monopoles.