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June 11th, 2015, 10:20 AM   #1
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Find solutions, that agrees with given conditions

For example I have this dif. equation:
4y''+4y'+y=0

I need to find a solution, with given conditions:
y(0) = 2
y'(0) = 0

So I solve that equation, get:
k1 = k2 = -0,5

So y = (C1+C2x)e^(-0,5x)

Now, to agree to those conditions, what I do:
y(0) = 2. I change x to 0 in y and get C1 = 2
Then I find derivative of y, do the same thing y'(0) = 0

Then I found C2. I put values of C1,C2 in y and that's the answer?
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June 11th, 2015, 12:46 PM   #2
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If I have not made a mistake , I found that $\displaystyle C_2=1$. So, you are right - just to substitute $\displaystyle C_1$ and $\displaystyle C_2$ with 2 and 1 respectively:
$\displaystyle y=(2+x)e^{-0.5x}$
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