Consider the following. (A computer algebra system is recommended.) 11y' − 2y = e−πt/2, y(0) = a...

Question

Question

Consider the following. (A computer algebra system is recommended.)

11y' − 2y = e^−πt/2, y(0) = a

(b) Solve the initial value problem. y(t) =

Find the critical value a₀ exactly. a₀ =

(c) Describe the behavior of the solution corresponding to the initial value a₀.

For a₀, the solution is y(t) =

Answer 1

Answer #1

,L/en (o) : a → 0 dy ot trun eary di忖erential na tHom and s 0 ol t 나ere PLE): P(t)d t The general asolutan o? t dt+ C ナC a 2 C. e → ae et

Answer 2

Similar Homework Help Questions

Consider the following. (A computer algebra system is recommended. Round your answers to four decimal places.)...

Consider the following. (A computer algebra system is recommended. Round your answers to four decimal places.) y' = 3 cos t − 6y, y(0) = 0 Please solve all parts of d) the equation and the evaluation of y(0.1)~y(0.4) Consider the following. (A computer algebra system is recommended. Round your answers to four decimal places.) y 3 cos t - 6y, y(0)0 (a) Find approximate values of the solution of the given initial value problem at t 0.1, 0.2, 0.3,...
16 Please help me solve the following Differential Equations problem Consider the following. (A computer algebra system is recommended.) x-(-1か 1 -4 (a) Find the general solution to the given sys...

16 Please help me solve the following Differential Equations problem Consider the following. (A computer algebra system is recommended.) x-(-1か 1 -4 (a) Find the general solution to the given system of equations x(t) = Describe the behavior of the solution as t O The solution diverges to infinity for all initial conditions. The solution tends to the origin along or asymptotic to 4 --) or asymptotic to ( O The solution tends to the origin along O The solution...
Describe the behavior of the solution corresponding to the initial value a. (a) 2y' − y...

Describe the behavior of the solution corresponding to the initial value a. (a) 2y' − y = e^t/3 , y(0) = a. (b) 3y' − 2y = e^−πt/2 , y(0) = a

please show all steps , thank you 6. Consider the initial value problem y" + 2y'...

please show all steps , thank you 6. Consider the initial value problem y" + 2y' + 2y = (t – 7); y(0) = 0, y'(0) = 1. a. Find the solution to the initial value problem. (10 points) b. Sketch a plot of the solution for t E (0,37]. (5 points) c. Describe the behavior of the solution. How is this system damped? (5 points)
please help with entire question 7(0) = -5. Consider the initial value problem 47" + 28y'...

please help with entire question 7(0) = -5. Consider the initial value problem 47" + 28y' +49-0, (0) - 1, (a) Solve the initial value problem. X(t) Plot its solution for osts 5. (A computer algebra system is recommended.) (b) Determine where the solution has the value zero. (c) Determine the coordinates (to, Yo) of the minimum point. (to yo)-( (d) Change the second initial condition to y(0) -b and find the solution as a function of b. Xt) Find...
Consider the initial value problem y'' – 2y' – 8y = 0, y(0) = a, y'(0)...

Consider the initial value problem y'' – 2y' – 8y = 0, y(0) = a, y'(0) = 6 Find the value of a so that the solution to the initial value problem approaches zero as t + oo Q = a =

Solve 2y'' – 5y' – 25y = 0, y(0) = -6, y'(0) = – 15 (t)...

Solve 2y'' – 5y' – 25y = 0, y(0) = -6, y'(0) = – 15 (t) = Consider the initial value problem y' + 3y' – 10y = 0, y(0) = a, y'(0) = 3 Find the value of a so that the solution to the initial value problem approaches zero as t + oo a = 1
(1 point) Find y as a function of lif y" - 11y +24y = 0 y(0)...

(1 point) Find y as a function of lif y" - 11y +24y = 0 y(0) - S WI) = 4 W = Remark: The initial conditions involve values at two points. Problem 4. (1 point) Find the solution to the linear system of differential equations 59x +84 -42x - 607 satisfying the initial conditions (0) = 10 and y(0) -7. = X(t) = y = Note: You can earn partial credit on this problem.
Consider the initial value problem y'' + 2y' – 15y = 0, y0) = a, y'0...

Consider the initial value problem y'' + 2y' – 15y = 0, y0) = a, y'0 = 1 Find the value of a so that the solution to the initial value problem approaches zero as t → a= Preview Get help: Video Points possible: 2 Unlimited attempts.

4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the...

4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...