Find the particular integral of the differential equation
d2y/dx2 + 3dy/dx + 2y = e −2x
(x + 1). show that the answer is yp(x) = −e −2x ( 1/2
x2 + 2x + 2) ]
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
Consider the differential equation
y '' −
2y ' + 10y =
0; ex
cos(3x),
ex
sin(3x), (−∞, ∞).
Verify that the given functions form a fundamental set of
solutions of the differential equation on the indicated
interval.
The functions satisfy the differential equation and are linearly
independent since
W(ex
cos(3x),
ex
sin(3x)) = _____ANSWER HERE______ ≠ 0 for −∞ <
x < ∞.
Form the general solution.
y = ____ANSWER HERE_____
Given the
complementary solution and the differential equation, Give the
particular and the total solution for the initial conditions.
Use C1 and C2 for the
weights, where C1 is associated with the root with smaller
magnitude. If the roots are complex, the complementary solution is
the weighted sum of complex conjugate exponentials, which can be
written as a constant times a decaying exponential times a cosine
with phase. Use C1 for the constant and Phi for the phase. (Note:
Some...
5. Consider the differential equation
xy^5/2 +1+x^2y^3/2dy/dx =0
(a) Show that this differential equation is not exact.
(b) Find a value for the constant a such that, when you multiply
the d.e. through by xa, it becomes exact. Show your working. Do NOT
solve the resulting differential equation.
6. Consider the differential equation
(D − 3)(D − 4)y = 0.
(a) Solve this d.e., showing brief working.
(b) How many solutions does this d.e. have? Justify your
answer.
(c) How...
Consider a nonhomogeneous differential equation
?′′ + 2?′ + ? = 2? sin?
(a) Find any particular solution ?? by using the method of
undetermined coefficients.
(b) Find the general solution.
(c) Find the particular solution if ?(0) = 0 and ?′(0) = 0.
A system is described by the differential equation
−5y′′(t)−3y′(t)+3y(t)=ys(t), Find the transfer function associated
with this system H(s). Write the solution as a single fraction in
s. H(s)=_______________?