y'' − 13 y' + 30 y = 30 e2 x + e 10 x cos(3 x)
x (0,0)=(3+4 sin cos e, +(3+4 sin º) sin 0 e2+ 4 cos 0 e3 The value of Jxoxxo/ at 9 = 1 is: 21 28 O 49
6. Solve the initial value problem y" + y = 0, y(0)=0, y'0=1 (a) -COS X (b) -sin x (c) -sin x + cos x (d) -sin x COS X (e) COS X (f) sin x (g) sin x-COS X (h) sin x + cos x 7. Find a particular solution yn of the differential equation (using the method of undetermined coefficients): y + y =p2 (a) 2e (b) 3e (c) 4e: (d) 6e (e) 2/2 (f) e2/3 (g) e2/4...
13) Show that y, = cos(In x) and y, = sin(In x)are independent solutions of x? y" + xy' + y = 0, and find the general solution of the equation.
7.12 The electric field of an elliptically polarized plane wave is given by [-k 10 sin(cot-kz-60°) E(z, t) y 30 cos(ot - kz)] (V/m). Determine the following: (a) The polarization angles (y, x). (b) The direction of rotation.
7.12 The electric field of an elliptically polarized plane wave is given by [-k 10 sin(cot-kz-60°) E(z, t) y 30 cos(ot - kz)] (V/m). Determine the following: (a) The polarization angles (y, x). (b) The direction of rotation.
show work
9. tan 37 10. sec 4 11. Find sin(x + y) and cos(x + y) if cosx = - cosy = -— x is in quadrant II and y is in quadrant III. [10] 12. Find the exact value of sin 2x and cos 2x if sin x = and cos x = - [6] 5 13. Simplify tan (x + 3) to a form involving sinx, cosx, and/or tanx. [6]
Using Matlab: If x(n) = cos(5π e-n/10) over n=[-10:30] and y(m)=sin(0.03πem/20) over m=[0:40], find z = x*y and its support vector k. Here * means convolution. Stem plot the results setting the axes using the command axis([-20,80,-2. .5,2.5]).
If sin(x) = 4/5 and cos(y) = 5/13 with both x and y terminating in quadrant 1 find the exact value of cos(x-y) I know that the denominator will be 65
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0
4. (a Let (sin( x cos( ) dr...
solve number 3
2. Show that u(x, y) = e = cos 12 + y2 is harmonic on the punctured complex plane D=C\{0}, and find a harmonic conjugate v of it. 1 2 3. Reveal, what is f(x) = u(x,y) + iv(I,y) in Problem 2?
Sin
and Cos
V15 13. Si sen(a) y está en el cuadrante III entonces sen 10 10 I. B. C.- 4 D. 4 4 14. cos(10")cos(59) + sen(10°)sen (5) = A) sen(5) B) cos(15) C) -cos(5) D) cos(59) 15. _1 + cot-(t) - csc (t) = A) 1 B) 4 C) 0 D) -1 16. 3 sen(x) + 2 sen(x + 2) = A) 5 sen(x) B) -5 sen(x) C) 5 sen(x) + 1 D) 5 sen(x) + 2