Please answer question fully Problem 2. Solve the following initial value problem y" + 2y +...
be quick please
2. Solve the following initial value problem * (8 Puan) = 8x2e-2y, y(0) = 1 dx O y = 1 In(4x4 + f2) O y = In(2x - 1) O y = -48x²e-2y O y = In(4x4 – 3) O y = {In(2x' + e?) O none of these O y = In(4x4 + 5) O y = 2x4 + e-2y+2 O y = In (2x + e)
2. Solve the initial value problem using method of Laplace transforms: y" + 2y' + 2y = 3e1 satisfying y(0) 0 y'(0) =-1
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Solve the initial value problem y" – 2y' + 5y = 0; y(0) = 2, y'(0) = -4. For answer from (a), determine lim y(t).
2. Solve the initial value problem = 4x + 2y, = 2x + y with r(0) = 1, y(0) = 0.
Question 9
In Exercises 7–11 solve the initial value problem. 7. y' – 2y = xy3, y(0) = 2/2 8. y' – xy = xy3/2, y(1) = 4 9. xy' + y = x4y4, y(1) = 1/2 10. y' – 2y = 2y1/2, y(0) = 1 11. y' – 4y = 402, y(0) = 1
exact differential equations
2. Solve the initial value problem: (2.1 – y) + (2y – r)y' = 0) with y(1) = 3. 3. Find the numerical value of b that makes the following differential equation exact. Then solve the differential equation using that value of b. (xy? + br’y) + (x + y)x+y = 0
Solve the given initial value problem. y" +2y' 26y 0; y(0) 2, y'(0)-1
Solve the initial-value problem. y" (0) =-1 y(0) = 2, y'(0) = 2, у",-2y" + y,-xe* + 5,
Solve the initial value problem y" – 3y' + 2y = e3r, y(0) = 2, y'(0) = -1. (a) y(x) = 40-1 – 4e2+ 2e 32 (b) y(x) = 1 e?' – 4e-2x + £230 (c) y(x) = 40-1 – 4e-2x + 3e3x (d) y(x) = 40" – 4e2x + e3r Select one: a с b d