Please...i have a test on monday...help?

Question

a)Solve the differential equation using the method of undetermined coefficient. Find the general solution.
y'' + 2y' + y = x*exp(-x), y(x) = yc(x) +?
b)y'' - 4y = exp(x)(cos(x)) , y(0) = 1 , y'(0) = 2 y(x)=?

i followed the rule did the subsitution but my answer is still wrong

Answer 1

Complimentary function
yc(x) = aexp(-x) + b x*exp(-x)

Usually you will choose trial particular integral as (A+Bx)*exp(-x)
but since both terms are already present in the complimentary function differentiating and substituting in the differential equation will not give you values for A and B. Therefore you should try multiplying this trial solution by x , x² ,.........

for example try

yp(x)= x*(A+Bx)*exp(-x)
that is
yp(x)= (Ax+Bx²)*exp(-x)
Hopefully you should be able to solve for A and B

for the second question

Complimentary function
yc(x) = aexp(-2x) + bexp(2x)

try trial particular integral

yp(x) = exp(x) [Acos(x) + Bsin(x)]

Differentiate and substitute in the given equation to find A and B.

Write the complete solution
y = yc(x) + yp(x)
and then apply the initial conditions to it in order
to find the constants from the complinentary function

Answer 2

The problem statement looks like it could be unclear. In some cases y or y' looks like a variable; in other cases it looks like either a function or a subscripted variable. Can you clarify the equations?

Answer 3

I am undecided as to how this is going to help you in your future.. but I sincerely hope that you find the answer to your question. I am baffled.. sorry to say. what level are you on.. as I usually can answer these things.. Must be very bright.. someone will help you..

Answer 4

change the ? to match your answer then you can be wright
right see how easy that is

1 plus 1 will alwas be 3 why

Answer 5

a) yc(x) = (A0 + A1*x) * exp(-x)
yp(x) = x^2 * (A2 + A3*x) * exp(-x)
y(x) = yc(x) + yp(x) = (A0 + A1*x + A2*x^2 + A3*x^3) * exp(-x)

b) yc(x) = A0*exp(2x) + A1*exp(-2x)
yp(x) = A2*exp(x)*cos(x) + A3*exp(x)*sin(x)

y(0) = A0 + A1 + A2 = 1
y'(0) = A0*2 - A1*2 + A2 + A3 = 2

A2 = 1 - A0 - A1
A3 = 1 - A0 + 3*A1