
3. (16) Find the general solution of y"+y = sec (r) tan (x). For each part below, circle your final answer. Find y Let th= 12 W 12 W = 0 f (2) 0 W = = = y = 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...
1. (3pts) Find the general solution of y(4) + 2y" + y = 0.
1. (3pts) Find the general solution of y(4) + 2y" +y=0.
(c) (i) Find the general solution of the following partial differential equation y, = 2y sin x + e-x Whatische solution when the initial conditions are v(0,y)--y, and (ii) y(x, 0) = cos x ? (10 Marks)
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...
Use the Method of Undetermined Coefficients to find the general solution for the differential equation: y"-2y'+2y= e^(x)sinx Answer should be: y= ce^(x)cosx+ce^(x)sinx-(x/2)e^(x)cosx
Detailed answer, showing the integration
4 Find the general solution for y" – 3y' +2y = 1+e-?
Find the general solution of y" + xy' + 2y = 0 in terms of power series in x. State the radius of convergence of the series.
Find the general solution, y(x) for (y')*(y'')+(y')3= 2e-2y