Solve (D2+2D+2)y=0
Initial Conditions: y(0)=1, y'(0)=2
1. Solve the equation y" + 4y' + 5y = 0 with the initial conditions y(0) = /2, y'(0) = -5.
Problem 3. Given the initial conditions, y(0) from t- 0 to 4: and y (0 0, solve the following initial-value problem d2 dt Obtain your solution with (a) Euler's method and (b) the fourth-order RK method. In both cases, use a step size of 0.1. Plot both solutions on the same graph along with the exact solution y- cos(3t). Note: show the hand calculations for t-0.1 and 0.2, for remaining work use the MATLAB files provided in the lectures
Problem...
y"+ 2y' + y = 0, y(0) = 1 and y(1) = 3 Solve the initial-value differential equation y"+ 4y' + 4y = 0 subject to the initial conditions y(0) = 2 and y' = 1 Mathematical Physics 2 H.W.4 J."+y'-6y=0 y"+ 4y' + 4y = 0 y"+y=0 Subject to the initial conditions (0) = 2 and y'(0) = 1 y"- y = 0 Subject to the initial conditions y(0) = 2 and y'(0) = 1 y"+y'-12y = 0 Subject...
1) Solve (D2-1)x + (D2-D)y =-2 sin t (D2 + D)x + D23/ = 0
solve it with matlab
25.24 Given the initial conditions, y(0) = 1 and y'(0) = 1 and y'(0) = 0, solve the following initial-value problem from t = 0 to 4: dy + 4y = 0 dt² Obtain your solutions with (a) Euler's method and (b) the fourth- order RK method. In both cases, use a step size of 0.125. Plot both solutions on the same graph along with the exact solution y = cos 2t.
Using the classical method, solve
if the initial conditions are
,
, and if the input if f(t)=u(t)
Do not use convolution.
(D? + 2D y(t) = (D+1) f(t) y(0) = 2 Y(0) = 1
Solve the next differential equation with initial
conditions y(0) = 1 and y'(0) = 1 by reducing it in order
−24y′ y′′ = −16y
OPTIONS
y= (1 3 y= (1+3) y = (1 + x) y (1 r) alic
y= (1 3 y= (1+3) y = (1 + x) y (1 r) alic
y"- y = 0 Subject to the initial conditions y(0) = 2 and y'(O) = 1 y"+y'-12y = 0 Subject to the initial conditions y(0) = 2 and y'(0) = 1
9) Using Euler method, solve this with following initial conditions that t = 0 when y = 1, for the range t = 0 to t = 1 with intervals of 0.25 dr + 2x2 +1=0.3 dt 1o) Using second order Taylor Series method, solve with following initial conditions to-0, xo-1 and h-0.24 11) x(1)-2 h-0.02 Solve the following system to find x(1.06) using 2nd, and 3rd and 4th order Runge-Kutta (RK2, RK3 and RK4)method +2x 2 +1-0.3 de sx)-cox(x/2)...
Solve the heat equation Ut = Uxx
+ Uyy on a square 0 <= x <= 2, 0<= y<= 2 with the
following boundary and initial conditions
2. Solve the heat equation boundary conditions uvw on a square O S r s 2, 0 S vS 2 with the (note the mix of u and tu) and with initial condition 0 otherwise Present your answer as a double trigonometric sum.
2. Solve the heat equation boundary conditions uvw on a...