What is the form of particular solution yp
(Y) that you would guess to solve the...
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
Solutions
Expert Solution
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Solution:-
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I am desperate to know How to find or guess Particular
solution(Yp) of Non-Homogeneous higher order differential
equations,
Please provide me with explanations.
There is Key Identities method also to find Yp. But I can't
understand.
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
Find the general solution y = C1Y1 +
C2 Y2 + Yp to the
ODE
y'' + y' − 2y = − 2x + 4 y (0) = − 4, y' (0) = − 7
Y = ?
Please show your work step by step. Thank you!
Find a particular solution yp of the following
EQUATIONS using the Method of Undetermined Coefficients. Primes
denote the derivatives with respect to x.
y''-16y=cos h(4x)
y''+36y=12cos(6x)+18sin(6x)
y''+4y'+8y=325e2tcos(5t)
y(5)+6y(4)-y=12
y(5)+2y(3)+2y''=8x2-2
SOLVE ALL ~ do ur besest (:
(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) Determine the correct form of the particular solution
y" + y = sin x
b) Solve IVP: y" + y = e^x + x^3; y(0) = 2, y'(0) = 0
c) Solve IVP: y" + y' -2y = x + sin 2x; y(0) = 1, y'(0) = 0