4. Solve the following initial value problems and sketch the solutions: (a) 4y" – 4y' +...
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0) = 1 by' + y - 6y = 0 y(0) = -1, y'(0) = 2 cy' + 4y + 3y = 0 y(0) = 1, y'(0) = 0 Problem 2: Solve the initial value problems: a y' +9y = 0 y(0) = 1. 1'(0) = -1 by" - 4y + 13y = 0 y(0) = 1, y'(0) = 3 cy" + ly + ly...
solve 5c 5. (24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y (1) = 0 (Bernoulli equation) 18 b) y" – 4y' – 12y = 3e5, y (0) =- (Hint: use the method of undetermined 7 coefficients) c) (2xy - 9x?) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE)
Solve the following initial value problems. When it is possible, express the solutions explicitly in terms of the independent variable. d) *– 4y = 3et, y(0) = -2, y'(0) = 0
B1: (24 marks) Solve the following initial value problems. When it is possible, express the solutions explicitly in terms of the independent variable. a) (t? + 1) 44 +3ty = 6t, y(0) = -1 b) * = y(1 – y), y(0) = 1/2 c) dy + +y = ty?, y(1) = 1 - 4y = 3e2t, y(0) = -2, y'(0) = 0
• 4. Solve the following initial value problem using Laplace transforms: y" – 4y' + 3y = 234, Y(0) = 0,5/(0)=1.
5 please and 17 only 3.2 Problems Find general solutions in powers of x of the diferential equa- tions in Problems 1 through 15. State the recurrence relation and the guaranteed radius of convergence in each case. 1, (x2-1 )y', + 4xy' + 2y = 0 2. (x2 + 2)y', + 4xy' + 2y = 0 3. y+xy y 0 4. (x2 + 1)y', + 6xy' + 4y = 0 5. (x2 3)y' +2xy 0 Use power series to solve...
Problem 3 Solve the initial value problems using Laplace Transforms (a) y' + 8y = t2 y(0) = -1 (b) y" – 2y' – 3y = e4t y(0) = 1, y'(0) = -1
Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8 Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0) = 8, y'(0) = 0 b) y" + 6y' + 13y = 12e-3xsin(2x), y(0) = 0, y'(0) = 0 (10 point) Find a general solution of each of the following nonhomogeneous equations. a) y" + 4y = 12x−8cos(2x) b) y(4)− 4y" = 16+32sin(2x)
(24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y(1) = 0 (Bernoulli equation) 18 1 b) y" – 4y - 12y = 3e St, y (0) = , y'(0) - (Hint: use the method of undetermined coefficients) c) (2xy - 9x) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE) = -1 7