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Find the general solution of the given second order differential equation. $$4y''+y'=0$$ This was my procedure to solving this problem:
$\chi(r)=4r^2+r=0$
$r(4r+1)=0$
$r=0, -\frac14$
$y_1=e^{0x}, y_2=e^{-\frac14x}$
And this led to get the answer,
$y=C_1+C_2e^{-\frac14x}$
I don't really have a question unless I solved this problem incorrectly. If someone could kindly check over my work to see if I did it right, that would be great!

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Should one of the variables by $y$ or $y''$? Right now it is first order, with solution any linear function as $y'=0$ –  Ross Millikan Oct 8 '13 at 18:18
    
You are missing $y''$. I believe it is $4y''$. –  Mhenni Benghorbal Oct 8 '13 at 18:18
1  
You can use Wolfram Alpha to check that your answer is right. wolframalpha.com/input/… –  Tyler Clark Oct 8 '13 at 19:55

2 Answers 2

up vote 1 down vote accepted

You are fine for the general solution, assuming the first term is $4y''$.

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hint you can reduce the order by putting

$$y'=w$$

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