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...
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
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...