SOLUTION: please help me answer this question:
Determine the particular solution of the equation,
{{{ d^2y/dx^2 + 4(dy/dx)= e^(-2x) }}}
given the initial conditions,
y(0)=0, y'(0)=0
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-> SOLUTION: please help me answer this question:
Determine the particular solution of the equation,
{{{ d^2y/dx^2 + 4(dy/dx)= e^(-2x) }}}
given the initial conditions,
y(0)=0, y'(0)=0
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Question 1115566: please help me answer this question:
Determine the particular solution of the equation,
given the initial conditions,
y(0)=0, y'(0)=0 Answer by math_helper(2461) (Show Source):
Now in the s-domain, we can write:
Solving for Y(s):
Using partial fraction expansion:
Multiplying both sides by (s)(s+2)(s+4) gives us:
This generates 3 equations in 3 unknowns:
from : A+B+C = 0 (1)
from : 6A+4B+2C = 0 (2)
from : 8A = 1 (3) —> A=1/8
Multiply (1) by 2 and subtract (2) to get: -4A-2B = 0, plug in A=1/8 to get B= -1/4
Now plugging in A=1/8, B=-1/4 into (1) and solving for C: C=1/8
Thus:
