# Second order linear DE

#### s7b

Hi,

I'm having problems solving this equation;

y'' -2y' +3y =0 y(0)=-1 , y'(0)=(root 2) -1

I found the auxiliary equation r^2 -2r +3 = 0
and since b^2 -4ac is less than zero this the case where r1 and r2 are complex numbers.

This is as far as I get without getting stuck.

Thanks :)

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#### rock.freak667

Homework Helper
For ay''+by'+cy=0

the auxiliary equation is ar2+br+c=0. If b2-4ac <0, such that the roots are in the form $r=M \pm Ni$

then y=eMx(Acos(Nx)+Bsin(Nx))

#### s7b

To find R1 and R2 do you just use the quadratic formula?

So r1= 1+i
and r2=1-i

#### rock.freak667

Homework Helper
To find R1 and R2 do you just use the quadratic formula?

So r1= 1+i
and r2=1-i
yep..so $r= 1 \pm i$ i.e. M=1 and N=1

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