1. (3pts) Find the general solution of y(4) + 2y" + y = 0.
1. (3pts) Find the general solution for the equation 2xy + y (No y' 4y4 + y2 need to write your solution in the explicit form.) 2. (3pts) Find the general solution of 2,4 = Express the general solution in the explicit form. 3. (4pts) Find the solution of the given initial value problem in explicit form: 3x2 2y – 3 1 y' =
2. (3pts) Find the general solution of y" – 54" + 6y = 0.
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...
4. (16) Find the general solution of y" - V - 2y = er for each part below, circle your final answer. Find y Let f(x) = W M12 Vs = 56) 1 - 0 W= (3) 42 General solution y =
(3 points) (a) Find the general solution to y′′+2y′=0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2. (3 points) (a) Find the general solution to y" + 2y' = 0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter cı as c1 and C2...
Find a solution 10. y" – 2y' + 2y = 2x, y(0) = 4, y'0) = 8.
1. Find the general solution to the equation y" - y - 2y = -e- 2. Find a particular solution to y" + 4y = 11 sin(2t) + cos(2t) 3. Find the form of a particular solution to be used in the Method of Undetermined Coefficients for the equation y" + 2y' +2y = te-* cost Do not solve the equation
Find the general solution of y" + xy' + 2y = 0 in terms of power series in x. State the radius of convergence of the series.
4. Find the solution to the differential equation y"+2y'+ 2y-S(t-) y(0) 0, y (0)-0 and graph it.