1. Find general solutions for the equations: (a) y" - 4y - 5y (b) y" +...
5. Find the general solution of the following differential equations: (a) 6"-5y y 0 (b) 4y"+12y9y 0 (c)2" 3y 6. Solve the following initial value problems:
4(10pt). Find the general solution for the following equations. (a) y) – 4y(3) + 5y" = 0. (b) z'y' - xy - y=0. (Hint: Use substitution v = Inx.)
Please show solutions.
Answer:
1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
Find the general solution of y” + 4y' + 5y = 0. Select one: • a. y = {-2x (cos(x) + sin(x)) b. y = e-24 (A cos(x) + B sin(x)) c.y = Cje-2x (cos(x) + sin(x)) O d. y = e*(A cos(2x) + B sin(2x))
[10] 6. Find the general solutions to the equations (a) 2x+y" + 5xy' + y = 0, (6) Y" – 2y + 5y = 3, YIV – 2k²y" + k*y = 0, (c) where k is a positive parameter.
[10] 6. Find the general solutions to the equations (a) 2.2 y' + 5.cy' + y = 0, (6) c) where k is a positive parameter. y" - 2y + 5y = 3, yl - 2k’y" +k y=0,
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...
non-homo 2nd order linear equations
1. Find the general solution for each of the following differential equations (10 points each): (a) (b) (e) y" – 2y! - 3y = 3e2x y" — y' – 2y = -2.3 + 4.2? y" + y’ – 67 = 1234 + 12e-2x y" – 2y' – 3y = 3.ce-1 y" + 2y' + y = 2e- (Hint: you'll use Rule 7. at least once) (e 2. Find the solution to the following differential equation...
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) = _______
Use the methods of section 8.2 to find the general solutions of the given systems of differential equations in the following three problems. dx 1. - x + y 2. = - 2x + y dt dy dx dt dy dt = 5x - 3y = -x + 4y dt 3. =- X - 4y dx dt dy dt = 2x + 3y