Question

In: Advanced Math

Consider the following initial value problem dy/dt = 3 − 2*t − 0.5*y, y (0) =...

Consider the following initial value problem

dy/dt = 3 − 2*t − 0.5*y, y (0) = 1

We would like to find an approximation solution with the step size h = 0.05.

What is the approximation of y(0.1)?

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Solve the following initial value problems (1) dy/dt = t + y y(0) = 1 so...
Solve the following initial value problems (1) dy/dt = t + y y(0) = 1 so y(t) = (2)  dy/dt = ty y(0) = 1 so y(t) =
Consider the system modeled by the differential equation dy/dt - y = t with initial condition y(0) = 1
Consider the system modeled by the differential equation                               dy/dt - y = t    with initial condition y(0) = 1 the exact solution is given by y(t) = 2et − t − 1   Note, the differential equation dy/dt - y =t can be written as                                               dy/dt = t + y using Euler’s approximation of dy/dt = (y(t + Dt) – y(t))/ Dt                               (y(t + Dt) – y(t))/ Dt = (t + y)                                y(t + Dt) =...
Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0)...
Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0) = 0, y(0) = 0
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y Initial conditions: x(0) = 0 y(0) = 2 a) Find the solution to this initial value problem (yes, I know, the text says that the solutions are x(t)= e^3t - e^-t and y(x) = e^3t + e^-t and but I want you to derive these solutions yourself using one of the methods we studied in chapter 4) Work this part out on paper to...
Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5
Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5
Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2...
Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2 if t>=3 }
Solve the following initial-value problem: (ye2xy + x)dx − (y2 − xe2xy)dy = 0, y(2) =...
Solve the following initial-value problem: (ye2xy + x)dx − (y2 − xe2xy)dy = 0, y(2) = 0
1. Consider the initial value problem y′ =1+y/t, y(1)=3 for1≤t≤2. • Show that y(t) = t...
1. Consider the initial value problem y′ =1+y/t, y(1)=3 for1≤t≤2. • Show that y(t) = t ln t + 3t is the solution to the initial value problem. • Write a program that implements Euler’s method and the 4th order Runke-Kutta method for the above initial value problem. Use your program to solve with h = 0.1 for Euler’s and h = 0.2 for R-K. • Include a printout of your code and a printout of the results at each...
Consider the following initial value problem. y''−4y = 0, y(0) = 0, y'(0) = 5 (a)...
Consider the following initial value problem. y''−4y = 0, y(0) = 0, y'(0) = 5 (a) Solve the IVP using the characteristic equation method from chapter 4. (b) Solve the IVP using the Laplace transform method from chapter 7. (Hint: If you don’t have the same final answer for each part, you’ve done something wrong.)
Consider the following differential equation: (t^2)y'-y=(y^2), where y'=dy/dt. (a) find y(t) if y(1)=1/2 (b)find limt->infinityy(t)
Consider the following differential equation: (t^2)y'-y=(y^2), where y'=dy/dt. (a) find y(t) if y(1)=1/2 (b)find limt->infinityy(t)
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT