Use method of undetermined coefficients to find a particular
solution of the differential equation ?′′ + 9? = cos3? + 2. Check
that the obtained particular solution satisfies the differential
equation.
Use the method of variation of parameters to find a particular
solution of the given differential equation and then find the
general solution of the ODE.
y'' + y = tan(t)
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...
Use the one solution given below to find the general solution of
the differential equation below by reduction of order method:
(1 - 2x) y'' + 2y' + (2x - 3) y = 0
One solution: y1 = ex
A. Find a particular solution to the nonhomogeneous differential
equation y′′ + 4y′ + 5y = −15x
+ e-x
y =
B. Find a particular solution to
y′′ + 4y = 16sin(2t).
yp =
C. Find y as a function of x if
y′′′ − 10y′′ + 16y′ =
21ex,
y(0) = 15, y′(0) = 28,
y′′(0) = 17.
y(x) =
Partial Differential Equations
(a) Find the general solution to the given partial differential
equation and (b) use it to find the solution satisfying the given
initial data.
Exercise 1. 2∂u ∂x − ∂u ∂y = (x + y)u
u(x, x) = e −x 2
Exercise 2. ∂u ∂x = −(2x + y) ∂u ∂y
u(0, y) = 1 + y 2
Exercise 3. y ∂u ∂x + x ∂u ∂y = 0
u(x, 0) = x 4
Exercise 4. ∂u...