# Second order differential equation

How do i solve the following equation?

u= L*(d^2i/dt)+ (1/c)*i r* (di/dt)

L= 1,4 mF
C= 0,31 H
R= 1000 ohm

Well i have so far found the auxiliary equation:
0,31*r^2 + 1000*r + 1/(1,4*10^-6)=0

And the discriminant is found to be 114286. This makes the form of the solution:

Y=c1*e^r1x + c2*e^r2x

I have found the roots:

r1=-1067,64
r2= -2158,18

But im stuck now and do not know what to do now.

Last edited:

LCKurtz
Homework Helper
Gold Member
Are you sure you have written the equation correctly? As written, it is not a constant coefficient equation and your "auxiliary equation" doesn't make sense.

HallsofIvy
Homework Helper
How do i solve the following equation?

u= L*(d^2i/dt)+ (1/c)*i r* (di/dt)
You mean u= l(d^2i/dt^2)+ (1/c)i+ r(di/dt)

L= 1,4 mF
C= 0,31 H
R= 1000 ohm

Well i have so far found the auxiliary equation:
0,31*r^2 + 1000*r + 1/(1,4*10^-6)=0
No, the auxiliary equation would be $1,4r^2+ 1000 di/dt+ 3.2= 0$. You are mixing up L and C.

And the discriminant is found to be 114286. This makes the form of the solution:

Y=c1*e^r1x + c2*e^r2x

I have found the roots:

r1=-1067,64
r2= -2158,18

But im stuck now and do not know what to do now.
What is u? A constant? If so, try a solution of the form i= A, a constant. What would A have to be to satisfy that equation?