1st- & 2nd-order differential eqns: ds/dt= u-gt, 60 d^2x/dt^2 + 500dx/dt + 900x = 0

jack1530

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1st- & 2nd-order differential eqns: ds/dt= u-gt, 60 d^2x/dt^2 + 500dx/dt + 900x = 0

i have been out of uni due to an operation and I have an exam coming up and have been completing past papers for revision, but i have gotten stuck with two equations and really dont know what to do, any help would be greatly appreciated as my course leader still hasnt replied.

the first equation is: ds/dt= u-gt i have to use separation of variables to determine a solution for s with respect to t, i know i need to get the s on one side and t on the other and integrate but have no idea where the u goes as i have not done one like this before.

the second is a second order and is 60 d^2x/dt^2 + 500dx/dt + 900x = 0

i need to find a general solution and i had started by using k to generate a quadratic but then couldnt get any further.

please any help is appreciated greatly as im awful at this
 
i have been out of uni due to an operation and I have an exam coming up and have been completing past papers for revision, but i have gotten stuck with two equations and really dont know what to do, any help would be greatly appreciated as my course leader still hasnt replied.

the first equation is: ds/dt= u-gt i have to use separation of variables to determine a solution for s with respect to t, i know i need to get the s on one side and t on the other and integrate but have no idea where the u goes as i have not done one like this before.

u is a value. Just keep it along for the ride. It is not one of your variables of interest and it is not a function of either of them.

jack1530 said:
the second is a second order and is 60 d^2x/dt^2 + 500dx/dt + 900x = 0

i need to find a general solution and i had started by using k to generate a quadratic but then couldnt get any further.

Did you find a characteristic equation and were you able to solve it?

jack1530 said:
please any help is appreciated greatly as im awful at this

I suggest not being awful. :)
 
i have been out of uni due to an operation and I have an exam coming up and have been completing past papers for revision, but i have gotten stuck with two equations and really dont know what to do, any help would be greatly appreciated as my course leader still hasnt replied.

the first equation is: ds/dt= u-gt i have to use separation of variables to determine a solution for s with respect to t, i know i need to get the s on one side and t on the other and integrate but have no idea where the u goes as i have not done one like this before.
\(\displaystyle \frac{ds}{dt}= u- gt\) is equivalent to \(\displaystyle ds= (u- gt)dt\) and then integrate both sides.

the second is a second order and is 60 d^2x/dt^2 + 500dx/dt + 900x = 0
If you try \(\displaystyle x= e^{at}\) then \(\displaystyle \frac{dx}{dt}= ae^{at}\) and \(\displaystyle a^2e^{at}\) so the equation becomes \(\displaystyle 60a^2 e^{at}+ 500a e^{at}+ 900e^{at}= e^{at}(60a^2+ 500a+ 900)= 0\). \(\displaystyle e^{at}\) is never 0 so we must have \(\displaystyle 60a^2+ 500a+ 900= 0\). Can you solve that equation


i need to find a general solution and i had started by using k to generate a quadratic but then couldnt get any further.

please any help is appreciated greatly as im awful at this
What do you mean by "using k"? Do you mean try \(\displaystyle e^{kx}\) so that you get the quadratic \(\displaystyle 60k^2+ 500k+ 900= 0\)? The first thing I would do is divide the equation by 20 to get \(\displaystyle 3k^2+ 25k+ 45= 0\). Then I would use the quadratic formula.
 
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