Find the general solution y(t) to the following ODE using (a)
Method of Undetermined Coefficients AND (b) Variation of
Parameters:
2y"-y'+5y = cos(t) - et Sin(t)
Use undetermined coefficients to solve the differential
equation. Linearly independent solutions to the associated
homogeneous ODE are also shown. (please provide a detailed
procedure to understand)
?2?′′ − 4??′ + 6? =
?4e-3x
y1=x2
y2=x3
a) Using the method of undetermined coefficients, find the
general solution of yʺ + 4yʹ −
5y = e^−4x
b) Solve xy'=(x+1)y^2
c) Solve the initial value problem :
(x−1)yʹ+3y= 1/ (x-1)^2 + sinx/(x-1)^2 ,
y(0)=3
Solve the given Boundary Value Problem. Apply the method
undetermined coefficients when you solve for the particular
solution.
y′′+2y′+y=(e^-x)(cosx−sinx)
y(0)=0,y(π)=e^π