For the following ODE i. Solve for x(t) Compare the values of x(0) and x(0 ii....
Problem 2.37 Solve the following problems for x(t). Compare the values of x (0+) and x (0). For parts (b) through (d), also compare the values of x (0+) and x(0 c.X+14x +49x = 3δ(t) x(0) = 2X(0) = 3
Problem 2.37 Solve the following problems for x(t). Compare the values of x (0+) and x (0). For parts (b) through (d), also compare the values of x (0+) and x(0 c.X+14x +49x = 3δ(t) x(0) = 2X(0) = 3
(a) Consider the following ODE ф" — 4ф + 4ф+ 0 (1) - with (0)(1)0 i. Put (1 into standard Sturm-Liouville form ii. Find the corresponding eigenvalue relation and eigenfunctions. Note that you do not have to normalise the eigenfunctions. (b) Solve the heat equation (2) 0<х<1 t>0 Ut u(0, t) u(1,t) u(x, 0) sin(2тx) + 1
(a) Consider the following ODE ф" — 4ф + 4ф+ 0 (1) - with (0)(1)0 i. Put (1 into standard Sturm-Liouville form ii....
Solve the following ode using Laplace transform: y' - 5y = f(t); y(0) - 1 t; Ost<1 f(t) = 0; t21
Solve the following 1st order ODE: * + 5x = cos(2t) x(0) = 2
We have this simple ODE model subject to x(0) = x0 ≥ 0, y(0) =
y0 ≥ 0 (you may choose values of x0 and y0). The constants α, β
> 0.
Question: Find an ODE for y(t) by eliminating x. Solve this ODE
analytically. Plot solutions using Mathematica.
x — ау dx dt dy dt = Вх y
1. a) Solve the following linear ODE. dy * dx + 2y = 4x2, x > 0 b) Solve the following ODE using the substitution, u = dy (x - y) dx = y c) Solve the Bernoulli's ODE dy 1 + -y = dx = xy2 ; x > 0
Use Laplace transformations to solve the following ODE for (t): ä(t) + 2r(t) = u(t) + 3u(t) Assume: u(t) = e- and initial conditions 2(0) = 1, +(0) = 0, u(0) = 0,
Solve the following ODE for y(x) y''+y'-2y=sin(2x) y(0)=2 y'(0)=0
any help on these two questions please??
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b) Find the general real solution of the linear ODE x(t)-Ax(t) + b(t). (c) Solve the initial value problem x(t) = A2(t) + b(t), x(0) = (-2,0,2)T 4.5: Determine the general solution of the ODE x"(t)-x"(t)-r(t) + x(t) = t cost.
4.4: Let 1 0 1 and b(t)- -1 1 0...
• 2. Find x in t = (0:1.5) by solving the ODE X' = f(t,x) = (t - y)/2 at * (t=0) = 1, using 4th-order RKM with At = 0.5 (home task).