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.
(a) Write a general expression for yp(x) a particular
solution to the nonhomogeneous
differential equation [Do not evaluate the coefficients]
y′′ + 2y′ + 2y = e-x (4x + sin x) + 2 cos(2x).
(b) Solve the initial value problem
y′′ - y = 1 + 4ex; y(0) = 1; y′(0) = 2:
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) =
How do you find the complementary solution of a nonhomogeneous
differential equation? Could someone give me a general rule or few
rules to find the complementary solution based on the appearance of
the given equation or the roots of the given equation? Thanks
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...
What differential equation is the one-dimensional potential
equation? What is the form of the solution of the one-dimensional
Dirichlet problem? The one-dimensional Neumann problem?
a) Determine whether the given differential equation is exact.
If it is exact, solve it. (If it is not exact, enter NOT.)
(2xy2 − 5) dx + (2x2y + 4) dy = 0
b) Solve the given differential equation by finding, as in
Example 4 of Section 2.4, an appropriate integrating factor.
(6 − 20y +
e−5x)
dx − 4 dy = 0