
Differential Equations Ordinary and Partial Differential Equations Math Forum 
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June 11th, 2015, 10:20 AM  #1 
Newbie Joined: Jun 2015 From: House Posts: 11 Thanks: 0  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? 
June 11th, 2015, 12:46 PM  #2 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 
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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