You are interesting me and also I need to know how to solve first order differential equations of higher degree
@carultch
9 ай бұрын
It's still the same fundamental idea. You just have a characteristic cubic (or higher degree polynomial), instead of a characteristic quadratic to solve. The idea is still to solve the equation assuming it's homogeneous, by assuming a solution of e^(r*t), and differentiating to match the original diffEQ. Then we solve for r, and construct an arbitrary linear combination of e^(r*t) based on all possible values of r. Similar procedures also apply for solving non-homogeneous diffEQs of higher order, by finding the particular solution and combining it with the homogeneous part.
@SkanCityAcademy_SirJohn
9 ай бұрын
Nice contribution.
@TheBaluchiterium
9 ай бұрын
You say "linear, because the coefficients are functions of x". But that is not the reason for the linearity of the DE. Even if the coefficients were not functions of x this equation would be a LDE. It is linear because the equation is a linear polynomial in the unknown function and its derivatives, i.e., the unknown function and all its derivative terms only appear to the maximum power of 1 (see also here en.wikipedia.org/wiki/Linear_differential_equation).
@SkanCityAcademy_SirJohn
9 ай бұрын
Thanks for your contribution, that is a great enlightenment. Thanks so much. Much love❤️
@mandandikaliyes847
11 ай бұрын
I enjoy your videos a lot 🇿🇲🇿🇲
@SkanCityAcademy_SirJohn
11 ай бұрын
Aww that's nice
@elliottemmanuel5137
Жыл бұрын
pls I'm looking for higher order differential equations do you have it on your playlist?
@SkanCityAcademy_SirJohn
Жыл бұрын
It's up to 2nd order DE
@AFCOE
Жыл бұрын
Very slow, calm and clear. ❤
@SkanCityAcademy_SirJohn
Жыл бұрын
That's great
@AFCOE
Жыл бұрын
@@SkanCityAcademy_SirJohn Good morning sir. Please sir am stock to solve. y"-2y'+y = ((3x^2)+1)e^x Am stuck on the particular integral. Thanks
@AFCOE
Жыл бұрын
Am letting Yp = (ax^2+bx+c)e^x. And it is giving. a=1/2, b(disappeared), c(disappeared). Please help me out❤
@SkanCityAcademy_SirJohn
Жыл бұрын
Okay, so once ax2.... Fails, you then try ax3... In that other until it matches up
@AFCOE
Жыл бұрын
Okay sir thanks very much. So there is no way to know what level to go..? ax^n at once?
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