4. (10 points) Solve the initial value problem xy' + 2y = ln(r), y(1) = 2...
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
2. Solve the following initial value problem: 3? - 2 + 3 4 + 2y and y(0) = 2. Your solution must be an explicit function (expressing y in term of r only) 3. Solve the Bernoulli equation: ry' + y = xy? Your solution must be an explicit solution, that is, you must write y as a function of
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
4) Solve the initial value problem by Laplace Transform (10 marks) y" - 2y' +y = te' y(0) = 1 %3D y'(0) = 1 %3D
1. (5 points) Use a Laplace transform to solve the initial value problem: y' + 2y + y = 21 +3, y(0) = 1,5 (0) = 0. 2. (5 points) Use a Laplace transform to solve the initial value problem: y + y = f(t), y(0) = 1, here f(0) = 2 sin(t) if 0 Str and f(0) = 0 otherwise.
Problem 7. [13 points; 4, 4, 5.] Consider the function f(r, y) 2y ln(r- ). (i) Find the unit direction of steepest increase for f at the point P (2, 1) (ii) Find the directional derivative of f at the point P(2,1) in the direction u = S (iii) Linearly approximate the value f((2,1)00) Problem 7. [13 points; 4, 4, 5.] Consider the function f(r, y) 2y ln(r- ). (i) Find the unit direction of steepest increase for f at...
Question 4 < > Solve the initial value problem below. x+y'' - xy' + y = 0, y(1) = – 5, y'(1) = 0 y
Solve the following initial value problem dy dc 2 +-y = ln(2), y(1) = 0.
Question 4 < > Solve the initial value problem below. xʻy" – xy' +y = 0, y(1) = – 5, y'(1) = 0 =