Solve the following initial value problem
x'(t) + y(t) = 2
y'(t) - x(t) = = δ(t − π)
x(0) = 0, y(0) = 1.
Solve the following initial value problem x'(t) + y(t) = 2 y'(t) - x(t) = =...
Use the Laplace transform to solve the given initial-value problem. y" + 4y' + 29y = δ(t-a) + δ(t-3x), y(0) = 1, y"(0) = 0 y(t) = Need Help? Read ItTalik to a Tutor Use the Laplace transform to solve the given initial-value problem. y" + 4y' + 29y = δ(t-a) + δ(t-3x), y(0) = 1, y"(0) = 0 y(t) = Need Help? Read ItTalik to a Tutor
3) Solve the following initial value problem. ( 1; 0 <t y" + y = f(t), y(0) = 2, y'(0) = -1, where f(t) = } nere -1; En VI t
Solve the following initial-value problem. y" + 3y + 4y = 282(t) - 385(t) y(0) = 1, y'(0) = -2
use laplace transform to solve initial value problem. thank you y(0) = 0 y(0) = 1, 11. y" + 4I/ + İSy = δ(t-n) + δ(t-37), r + -2(t-r) sin 3 (t- y(0) = 0 y(0) = 1, 11. y" + 4I/ + İSy = δ(t-n) + δ(t-37), r + -2(t-r) sin 3 (t-
7. Solve the initial value problem --( y = -1 00 when the initial value is given as following: and discuss the behavior of the solution as t (you may sketch the solution curve.) (a) X(0) = (0,0.5). 7. Solve the initial value problem --( y = -1 00 when the initial value is given as following: and discuss the behavior of the solution as t (you may sketch the solution curve.) (a) X(0) = (0,0.5).
Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(t)-7, o s t Plot the solution for varying tolerances. Why do you believe your solution is cor- 2. 1, y(0)-0, y,(0) 1, y"(0)-0. rect? Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(t)-7, o s t Plot the solution for varying tolerances. Why do you believe your solution is cor- 2. 1, y(0)-0, y,(0) 1,...
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0
[10] 2. Solve the initial value problem (x² + 3y² + x)y' + 2xy + y = 0, y(1) = 1.
Solve the following initial value problem. St/2 if 0 <t<6 y" +y= 3 ift > 6 6 y(0) = y'(0) = 0 14Pm1011* 1917 Prid A++ V "Top14