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...
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) Find the right form of the particular solution (you don't have to solve it)
y''-6y'+9y=6x^2+2-12e^3x
b) Solve using variation of parameters
y" + y = secx
c) define or explain the following
- Linear system
- Linear Homogenous system
- Linear Homogenous system with Constant coefficients
d) Solve the initial value problem using the D elimination
dx/dt = 4x - 3y
dy/dt = 6x-7y
Subject to the I.C
x(0) = 2
y(0) = -1
Use the annihilator method to write the form of the particular
solution but do not solve the differential equation
1. y”+y=e^(-x)+x^2
2. y”’+y=xe^(2x)cosx+sinx
Find the general solution
1. y”-2y’-8y=4e^(2x)-21e^(-3x)
Find the general solution of the given differential equation.
Then find the solution that passes through the given initial
solution
1. y”+6y+10y=3xe^(-3x)-2e^(3x)cosx, y(0)=1, y’(0)=-2
What is the form of particular solution yp
(Y) that you would guess to solve the following equation using the
Method of Undetermined Coefficients? Write yp
with appropriate constants, but DO NOT solve for the constants
y ′′ −3y ′ +2y =
t2et cost
+ te2t
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.
(a) y′′ +10y′ +25y=2e^(5t) +te^(−5t)
b) y′′ +9y=5t^2 +4cos(3t)+6e^(3t)
Using the method of undetermined coefficients determine the
exact (only) of a particular solution. Do not evaluate the
coefficients.
y''' + 2y'' + y' = 5e-tsin(t) + 3 +
7te-t
Translate the following argument into symbolic form and
determine weather it's logically correct by constructing a truth
table. Money causes all the world's troubles or money helps the
poor. If money helps the poor, it is not the cause of all the
worlds troubles. Money is the cause of all the world's troubles.
Therefore, money does not help the poor. Please show how the
problem was solved!