Show all work for each problem. 1. (15 pts) y"-2y'+2y = 2x, y(0) = 4, y"0)...
Find the solution of the given initial value problem: y(4) + 2y" + y y(3) (0) y, (0) 0, y', (0) llt + 2; y (0) 1 Enclose arguments of functions in parentheses. For example, sin (2x) Find the solution of the given initial value problem: y(4) + 2y" + y y(3) (0) y, (0) 0, y', (0) llt + 2; y (0) 1 Enclose arguments of functions in parentheses. For example, sin (2x)
8. Find the solution to the differential equation y"+2y'+y=sinx using the method of undetermined coefficients. 1 COS X (a) y=ce' +ce' + -cosx 2 (b) y = ce' +cxe'+ (c) y = cxe' +cze cos x (d) y= c,e* + c xe" COSX 1 (e) y=ce' + ce + sinx 2 (f) y=ce' + exe* + sin x 2 (g) y=cxe' + e*- sinx 2 (h) y=ce' + cxe' 1 sinx 9. Use the method of undetermined coefficients to find...
Chapter 3, Section 3.5, Question 15 Find the solution of the initial value problem y" + 2y' + 5У-16e-t cos (2t), y (0)-4, y, (0-0. Enclose arguments of functions in parentheses. For example, sin (2x) Equation Editor Ω Common Matrix 亩。 sin(a) ca) tanta) sec(a) ese(a cot(a sin (a) y (t) Click if you would like to Show Work for this question: Open Show Work Chapter 3, Section 3.5, Question 15 Find the solution of the initial value problem y"...
We consider the non-homogeneous problem y" + 2y + 2y = 40 sin(2x) First we consider the homogeneous problem y" + 2y + 2y = 0: 1) the auxiliary equation is ar? + br +C = 242r42 = 0. 2) The roots of the auxiliary equation are 141-14 Center answers as a comma separated list). 3) A fundamental set of solutions is -1 .-1xco) Center answers as a comma separated list. Using these we obtain the the complementary solution y...
Q4 please 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find a particular solution of the equation y" +2/ +2y = sin 2x by method of undetermined coeficients. 4 marks] (c) Use Laplace transform to solve the initial value problem l-1, 21 0-,0)- [10 marks] 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find...
3) Solve the initial value problem. a) nie - 2x(y2 – 2y) = 0, with y(0) = 4 b) (-4y cos x + 4 sin I Cos I + sec? x)dx + (4y - 4 sin x)dy = 0, with y ) = 1
Find a solution 10. y" – 2y' + 2y = 2x, y(0) = 4, y'0) = 8.
Find the solution of the given initial value problem in explicit form. y′=(9x)/(y+x^2y), y(0)=−3 Enclose arguments of functions in parentheses. For example, sin(2x).
7. Given that y(x) = sin 2x is a particular solution to y" + 2y + 4y - 4 cos 2x = 0, find the general solution.
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...