# Thread: Transfer function by differential equation

1. ## Transfer function by differential equation

How can I obtain the transfer function of system Y(s)/ X(s), which has the differential equation below ?

d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

If possible give me a tip to insert special characters here, as pi and division sign with a number over the other

2. Originally Posted by moisesbr
How can I obtain the transfer function of system Y(s)/ X(s), which has the differential equation below ?

d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

If possible give me a tip to insert special characters here, as pi and division sign with a number over the other

For mathematical type setting we use LaTeX, the tutorial is here

CB

3. Originally Posted by moisesbr
How can I obtain the transfer function of system Y(s)/ X(s), which has the differential equation below ?

d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

If possible give me a tip to insert special characters here, as pi and division sign with a number over the other

Write this as:

$\displaystyle D^3y+3D^2y+5Dy+y=D^3x+4D^2x+6Dx+8x$

Then if we assume that at time $\displaystyle t=0$ that the input and out put and all relevant derivatives are zero, and we take the Laplace transform of the above equation we get:

$\displaystyle s^3Y(s)+3s^2Y(s)+5sY(s)+Y(s)=s^3X(s)+4s^2X(s)+6sX( s)+8X(s)$

then the transfer function is:

$\displaystyle T(s)=\frac{Y(s)}{X(s)}=\frac{s^3+4s^2+6s+8}{s^3+3s ^2+5s+1}$

CB

4. How did you pass from first to second line below ?

Sorry for the silly question but I've been a long time out of maths
and I having a hard time to remind all in a new course I am starting

d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*x/dt^3 + 4(d^2* x/dt^2) + 6(dx/dt) + 8x

5. Originally Posted by moisesbr
How did you pass from first to second line below ?

Sorry for the silly question but I've been a long time out of maths
and I having a hard time to remind all in a new course I am starting

$\displaystyle D^n \equiv \frac{d^n}{dt^n}$