Ploting some ode's solution.

hello. I want to plot some graph that ode(ordinary differential equation)'s solution(I will make this solution to polynomial from exponential with Taylor Series) . How can I plot that? How can I code it?

y''-5y'+4y = 0

Answer 1

[Torsten]

The general solution is

y(t) = C1*exp(4*t) + C2*exp(t)

for arbitrary constants C1 and C2.

Look up "dsolve" and the examples provided under

https://de.mathworks.com/help/symbolic/dsolve.html

[Yeachan Choi]

hey, Thx But I should take this solution to polynomial eqn from exp with Taylor series... How can I do that???

[Torsten]

Not clear. Include your precise assignment question.

[Yeachan Choi]

I mean, I will ploting (y''-5y'+4y = 0)'s solution, y(t) = C1*exp(4*t) + C2*exp(t). But I want to make this for polynomial equation. (I will use Taylor Series.)

[Torsten]

I don't understand

But I want to make this for polynomial equation. (I will use Taylor Series.)

Can you give an example ?

[Yeachan Choi]

your solution is exponential function right? But I want to make your solution to be a polynomial function, so I will use Taylor Series in matlab

[Torsten]

So you want to make the ansatz

y(t) = sum_{i=0}^{i=oo} a_i * t^i

and determine the coefficients a_i ?

[Yeachan Choi]

I will give C1 C2 and the other coefficients as a randi(). So I need the code for Taylor series.

[Torsten]

I give up.

All solutions to the equation

y''-5y'+4y = 0

are given by

y(t) = C1*exp(4*t) + C2*exp(t)

for constants C1 and C2.

There are no polynomial solutions, except for the case that C1 = C2 = 0.

So I can't understand what you mean "you want to make the solution a polynomial function".

Of course, you can do

syms C1 C2 t
f = C1*exp(4*t) + C2*exp(t);
taylor(f,t,'Order',8)

but why ?

[Yeachan Choi]

haha But Thank you.