Using Euler method, ODE45 and Simulink solve the following ODE's.
a) y+c(dy/dt)=10sinwt
c=2, w=10, y(0)=0
Assume time span 0: 0.01: 10
b) dy/dt=t^2+yz
dz/dt=t+y^2z^2
y(0)=0.2
z(0)=-0.1
Assume time span 0: 0.1 :1
c)(d^2)y/dt^2+0.5(dy/dt)+siny=0
y(0)=1
dy/dt =0 when t=0
assume time span 0: 0.01 :10
Matlab code please
Consider the non linear ODE:
(dx/dt) = -y = f(x,y)
(dy/dt) = x^2-x = g(x,y)
(a). Compute all critical points (b) Derive the Jacobian matrix
(c). Find the Jacobians for each critical point (d). Find the
eigenvalues for each Jacobian matrix (e). Find the linearized
solutions in the neighborhood of each critical point (f) Classify
each critical point and discuss their stability (g) Sketch the
local solution trajectories in the neighborhood of each critical
point
Use euler method to approiximate y(1)
y' is given , solve for y. approiximate y(1)
Create a table to show the approximate value of y(1) for each
choice of h.
y’ = -15y y(0) = 1
h = .25
h = .125
h = .0625
h = .03125
Consider the following initial value problem
dy/dt = 3 − 2*t − 0.5*y, y (0) = 1
We would like to find an approximation solution with the step
size h = 0.05.
What is the approximation of y(0.1)?