16. Consider the intial value problem a.) Use the MATLAB program myeuler,m to co

Question

16. Consider the intial value problem

a.) Use the MATLAB program myeuler,m to compute Euler Method approximation to y(t) with step size h = 0.2 and n = 10 steps. The program will generate a list of ordered pairs. (ti, yi). Use plot to graph the piecewise linear function connecting the points (ti,yi). What appears to be happening to y as t increases?

16. Consider the intial value problem dy/dt = 2y - 2 + 3e-t, y(0) = 0 a.) Use the MATLAB program myeuler,m to compute Euler Method approximation to y(t) with step size h = 0.2 and n = 10 steps. The program will generate a list of ordered pairs. (ti, yi). Use plot to graph the piecewise linear function connecting the points (ti,yi). What appears to be happening to y as t increases?

Explanation / Answer

y' -y =3e^t +18e^7t

this is a linear differential equation:

y=e^[-A(t)]*[? e^(A(t))*b(t) dt + C]

a(t)=-1
A(t)=-t
b(t)=3e^t +18e^7t

? e^(-t)*(3e^t +18e^7t) dt

? 3+18e^6t dt

3t +3e^6t

y=e^(t)[3t +3e^6t + C]

y=Ce^t +3te^t +3e^7t

y=Ce^t +3e^t(t +e^6t)

y(0)=2

2=Ce^0 +3e^0[0+e^(6*0)]
2=C+3
C=-1

y=-e^t +3e^t[t+e^6t]

y=e^t[3t+3e^6t -1]

please what? Here is the answer: y=e^t[3t+3e^6t -1]

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