13) Show that y, = cos(In x) and y, = sin(In x)are independent solutions of x?...
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, 0). Find the general solution of the given nonhomogeneous equation. *?y" + xy' + (x2 - 1)y = x3/2; Y1 = x-1/2 cos(x), Y2 = x-1/2 sin(x) y(x) =
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...
o2: 16 Marks] Find the general solution of the differential equation (sin x)y" +(cos x)y' cos x by reduction to first order DE. o2: 16 Marks] Find the general solution of the differential equation (sin x)y" +(cos x)y' cos x by reduction to first order DE.
Show that sin (kx) and cos (kx) given in Eq. (11-48a) are two independent solutions of the differentia equation, Eq. (11-47a). Consider a rectangular wavequide haing dimoneinc 404 We were unable to transcribe this image(11-48a) X(x)- Asin(k,x)+B cos (k,x)
Find all solutions of the equation in the interval (0,2). cos 5x cos x+ sin 5x sinx=0 Write your answer in radians in terms of it. If there is more than one solution, separate them with commas. 8 000
Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. xy) =x"cos(y) +x"win(x) cos(x)sin(y). Plo The direction in which the given function txy_f(xy)-x3cos(v)+x2vsin(x) + cos(x)sin(y)increases most rapidly at P 0주 is u: " (Type exact answers, using radicals as n (xy)=x3cos(y)+x"win(x)-cos(x)sin(y) The direc on in which the given function f(xy- is eases most rapidly at (Type exact answers, using radicals as needed The derivative of the...
Solve i. and ii. Given the ordinary differential equation: cos(x)y' = sin(x)y + 1 Find the general solution of the given differential equation. ii. Solve the ordinary differential equation: ay' + by = a cos(wx) + Bsen(wx) Where: a, b, a,ß and w are nonzero real constants.
4. Given that {cos x, sin 2, 1) is a fundamental set of solutions for y" + y = 0, solve the initial value problem with conditions y(0) = 3, y'(0) = 5, "(0) = -4. 4. Given that {coso, sin x 1} is a fundamental set of solutions for y'" + y = 0, solve the initial value problem with conditions y(0) - 3, V'(0) -- 5. "(0) -4
For cos x cos 3x – sin x sin 3x = 0, use an addition or subtraction formula to simplify the equation and then find all solutions of the equation in the interval x (0,7). The answer is 21 22 = 23 = and 14 with xi < 22 <<3 < 24.
Verify that yi = XpJp(x) and y, = xryp(x) are linearly independent solutions of xy" + (1-2p)y, + xy = 0, x>0. 4. Verify that yi = XpJp(x) and y, = xryp(x) are linearly independent solutions of xy" + (1-2p)y, + xy = 0, x>0. 4.