(17 points) (a) Find the general solution of the differential equation y" (t) + 36y(t) =...
(17 points) (a) Find the general solution of the differential equation y" (t) + 4y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (i) y(0) = 0, y'(0) = 1: y = (ii) y(0) = 1, y'(0) = 0:y= (iii) y(0) = 1, y(1) = 0:y= (iv) y(0) = 0, y(1) = 1: y = (On a...
(5 points) Find the general solution to the differential equation y" – 2y + 17y=0. In your answer, use Cį and C2 to denote arbitrary constants and t the independent variable. Enter Cų as C1 and C2 as С2. y(t) = help (formulas) Find the unique solution that satisfies the initial conditions: y(0) = -1, y'(0) = 7. y(t) =
Find a general solution to the differential equation. y" - y = - 13t+4 The general solution is y(t) = (Do not use d, D, E, E, I, or I as arbitrary constants since these letters already have defined meanings.)
5. Given the differential equation: e(dy/dx) 2x (a) Find the general solution (b) Graph particular solutions for integration constants C-0, 5, 10 and 15. You can put all plots on one graph or prepare separate plots. Show all calculations 5. Given the differential equation: e(dy/dx) 2x (a) Find the general solution (b) Graph particular solutions for integration constants C-0, 5, 10 and 15. You can put all plots on one graph or prepare separate plots. Show all calculations
Find a general solution to the differential equation. y'' - y= - 19t + 6 The general solution is y(t) = (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
1.Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .2.Solve the given initial value problem. y'' + 3y' = 0; y(0) = 12, y'(0)= - 27 The solution is y(t) = _______ 3.Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them z"'+z"-21z'-45z = 0 A general solution is z(t) = _______
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
MATLAB HELP (a) Use the command dsolve to find general solutions to the differential equations below. i. y 00 + 3y = 0 ii. y 00 + 4y 0 + 29y = 0 iii. y 00 − y/36 = 0 iv. y 00 + 2y 0 + y = 0 v. y 00 + 6y 0 + 5y = 0 (b) Graph each of the solutions in (a) in the same window with 0 ≤ t ≤ 10, using the...
Find a general solution for the given differential equation with x as the independent variable. y (4 + 2y'"' + 377"' +72/' + 36y = 0 A general solution with x as the independent variable is y(x) =
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.