Consider the following second-order ODE: (d^2 y)/(dx^2 )+2
dy/dx+2y=0 from x = 0 to x =...
Consider the following second-order ODE: (d^2 y)/(dx^2 )+2
dy/dx+2y=0 from x = 0 to x = 1.6 with y(0) = -1 and dy/dx(0) = 0.2.
Solve with Euler’s explicit method using h = 0.4. Plot the x-y
curve according to your solution.
Consider the following first-order ODE dy/dx=x^2/y from x = 0 to
x = 2.4 with y(0) = 2. (a) solving with Euler’s explicit method
using h = 0.6 (b) solving with midpoint method using h = 0.6 (c)
solving with classical fourth-order Runge-Kutta method using h =
0.6. Plot the x-y curve according to your solution for both (a) and
(b).
d^2y/dx^2 − dy/dx − 3/4 y = 0,
y(0) = 1, dy/dx(0) = 0,
Convert the initial value problem into a set of two coupled
first-order initial value problems
and find the exact solution to the differential equatiion
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