5. Solve equation y'+2y=2-e^-4t, where y(0)=1 6. Use Euler’s method for a previous problem at t=0,...

5. Solve equation y'+2y=2-e^-4t, where y(0)=1

6. Use Euler’s method for a previous problem at t=0, 0.1, 0.2, 0.3. Compare approximate and the exact values of y.

Expert Solution

milcah answered 2 years ago

u(t−c) =uc(t) ={0, 0≤t<c,1, t≥c.} USE Laplace Transform to solve y′′+ 2y′+ 2y=δ(t−5)e^tcost, y(0) = 1,...

u(t−c) =uc(t) ={0, 0≤t<c,1, t≥c.} USE Laplace Transform to solve y′′+ 2y′+ 2y=δ(t−5)e^tcost, y(0) = 1, y′(0) = 2, whereδ(t)is the Dirac delta. Does the solution show a resonance?

y'' - y = e^(-t) - (2)(t)(e^(-t)) y(0)= 1 y'(0)= 2 Use Laplace Transforms to solve....

y'' - y = e^(-t) - (2)(t)(e^(-t)) y(0)= 1 y'(0)= 2 Use Laplace Transforms to solve. Sketch the solution or use matlab to show the graph.

Solve the differential equation by Laplace transform y^(,,) (t)-2y^' (t)-3y(t)=sint where y^' (0)=0 ,y=(0)=0

y"-3y'+2y=4t-8 , y(0)=2 , y'(0)=7 y(t)=?

Euler’s method Consider the initial-value problem y′ = −2y, y(0) = 1. The analytic solution is...

Euler’s method Consider the initial-value problem y′ = −2y, y(0) = 1. The analytic solution is y(x) = e−2x . (a) Approximate y(0.1) using one step of Euler’s method. (b) Find a bound for the local truncation error in y1 . (c) Compare the error in y1 with your error bound. (d) Approximate y(0.1) using two steps of Euler’s method. (e) Verify that the global truncation error for Euler’s method is O(h) by comparing the errors in parts (a) and...

y''+ 3y'+2y=e^t y(0)=1 y'(0)=-6 Solve using Laplace transforms. Then, solve using undetermined coefficients. Then, solve using...

y''+ 3y'+2y=e^t y(0)=1 y'(0)=-6 Solve using Laplace transforms. Then, solve using undetermined coefficients. Then, solve using variation of parameters.

Question

5. Solve equation y'+2y=2-e^-4t, where y(0)=1 6. Use Euler’s method for a previous problem at t=0,...

Solutions

Expert Solution

Related Solutions

u(t−c) =uc(t) ={0, 0≤t<c,1, t≥c.} USE Laplace Transform to solve y′′+ 2y′+ 2y=δ(t−5)e^tcost, y(0) = 1,...

y'' - y = e^(-t) - (2)(t)(e^(-t)) y(0)= 1 y'(0)= 2 Use Laplace Transforms to solve....

Solve the differential equation by Laplace transform y^(,,) (t)-2y^' (t)-3y(t)=sint where y^' (0)=0 ,y=(0)=0

y"-3y'+2y=4t-8 , y(0)=2 , y'(0)=7 y(t)=?

Euler’s method Consider the initial-value problem y′ = −2y, y(0) = 1. The analytic solution is...

y''+ 3y'+2y=e^t y(0)=1 y'(0)=-6 Solve using Laplace transforms. Then, solve using undetermined coefficients. Then, solve using...

Use the Laplace transform to solve the problem with initial values y''+2y'-2y=0 y(0)=2 y'(0)=0

Solve the differential equation y''+y'-2y=3, y(0)=2, y'(0) = -1

y''' + 2y'' − y' − 2y = sin(4t), y(0) = 0, y'(0) = 0, y''(0) = 1

Solve the equation below for y(t): y''+2y'-3y=8u(t-3): y(0) = 0; y'(0)=0