y"+y'-6y=1
1. general solution of corresponding homogenous equation
2. particular solution
3.solution of initial value problem with initial conditions
y(0)=y'(0)=0
y"-2y'+y=cos2t
1. general solution of corresponding homongenous equation
2. particular solution
3.solution of initial value problem with initial conditions
y(0)=y'(0)=0
1. solve the initial value problem.
(t^(2)+1)y'+2ty=tant , y(0)=2
2.find the solution to this initial value problem.
yy'=e^x+x , y(0)=y_0
y_0 is a nonzero constant.
Consider an initial value
problem
?′′ + 2? = ?(?) = cos? (0 ≤ ? < ?) , 0 (? ≥
?)
?(0) = 0 and ?′(0) = 0
(a) Express ?(?) in terms of the unit step function.
(b) Find the Laplace transform of ?(?).
(c) Find ?(?) by using the Laplace transform method.
y'''-2y"-y'+2y=xex^2+2x
a) Find a general solution to the corresponding homogeneous
equation, given that e2x is one.
b) In the method of variation of parameters, find v1,
where v1e2x + v2y2 +
v3y3 = yp is a particular solution
to the inhomogeneous equation. Use the method of variation of
parameters
Please explain and show work, thanks!