Exponential Response - Possible Resonance

[@chnegsi]

'we have to drag L'Hopital from hospital and do it again...' LOL

[@shreyanand2226]

🤣🤣🤣🤣

[@francine8563]

thank you so much sir! Heroes truly don't wear capes, heroes are the educators!

[@atomskyjahid1533]

Throughout these lectures, I felt like I'm relearning physics. :)

[@hathuytu]

this way of solving the ode could lead to the case that y= -t*exp(s1*t)/(2A*s1+B) is also a perticular solution. It looks like this is a trick, not a method to solve this ode. There are two other perticular solutions as well.

[@Z-eng0]

But where did the 2nd e^s1t go ? And does the 1/(2As1 + B) give us a 1 ?

[@Labroidas]

I really didn't get that last part at all. I feel like there is a hole in the explanation, the video is over a little too quick. I tried solving my homework with this method and it didn't work at all for me.

[@gabrielbrunoparreira5670]

kind of late response so you probably already figured it out by now haha. But anyways this is how I understand it: It seemed like they were more like partial derivatives. He derived the functions with respect to s and treated t as a constant. That is why on the first one you have the exponential multiplied by t. The second equation would be just a constant because s1 is a constant and t is also a constant, so the derivative is 0.

[@rakhimovv]

In case of resonance: y(t) = y_null + y_particular = c_1 * e^{s_1*t} + c_2 * e^{s_2*t} + c_3 * t * e^{s_1*t}. Further if also s2=s1 then: y(t) = y_null + y_particular = c_1 * e^{s_1*t} + c_2 * t* e^{s_1*t} + c_3 * t^2 * e^{s_1*t}.

[@QuranTilwatAndTranslation]

can you contact me i am expert of integeration and differention . i have some new theorms