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Second Order Differential Equation Question

Hi,

I was working on the following 2nd order DE question

Find the general solution of

d2ydx2−6dydx+9y=0\frac{d^{2}y}{dx^{2}}-6\frac{dy}{dx}+9y=0

Using the auxilliary equation

n2−6n+9=0n^{2}-6n+9=0

I got the value of n to be 3 (a repeated root)

And the answer to be

y=(A+Bx)e3xy=\left( A+Bx \right)e^{3x}

However, the textbook says the answer is

y=(A+Bx)e−3xy=\left( A+Bx \right)e^{-3x}

Have I done something wrong?

Any help would be appreciated :smile:
(edited 10 years ago)
Reply 1
Avatar for bijesh12
bijesh12
13
Original post by alow
Hi,

I was working on the following 2nd order DE question

Find the general solution of

d2ydx2−6dydx+9y=0\frac{d^{2}y}{dx^{2}}-6\frac{dy}{dx}+9y=0

Using the auxilliary equation

n2−6n+9=0n^{2}-6n+9=0

I got the value of n to be 3 (a repeated root)

And the answer to be

y=(A+Bx)e3xy=\left( A+Bx \right)e^{3x}

However, the textbook says the answer is

y=(A+Bx)e−3xy=\left( A+Bx \right)e^{-3x}

Have I done something wrong?

Any help would be appreciated :smile:


No you are right, probably a typo.
Reply 2
Avatar for alow
alow
OP
19
Original post by bijesh12
No you are right, probably a typo.


Thanks! I thought that was probably it, but just wanted to be sure :smile:

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