4. Verify that yi xPJp(x) and y2 - xPYp(x) are linearly independent solutions of xy" + (1-2 )y, +...
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.
4. Find two linearly independent series solutions of y" + x²y' + xy = 0 (description of the series up to degree 6 is enough.)
4. Find two linearly independent series solutions of y" + x²y' + xy = 0 (description of the series up to degree 6 is enough.)
Problem #1 Y1(x)= x and Y2(x)=e* are linearly independent solution of the homogeneous equation: (x-1)y"-xy'+y = 0 Find a particular solution of (x-1) y”-xy’+y = (x-1)} e2x
Two linearly independent solutions of the differential equation y''+4y'+4y=0 are of Two linearly independent solutions the differential equation are 2x y,=e Y2 = e 2x / - 2x 6 Y,=e 92= xe 2x @g, = e - 2x -2x , 92= xe 2x y = e 2x Y 2 = xe²x e 9,=02x 1 Y 2 = e- 2x
Two linearly independent solutions of the differential equation y" - 5y' + 6y = 0 are Select the correct answer. a. Y1 = 62, y2 = 232 b. Y1 = 0 -6x, y2 = e** c. Y1 = e-Gx, y2 = et d. Y1 = 0-2, y2 = 2-3x e. Yi = e6x, y2 = e-*
Two linearly independent solutions of the differential equation y" + 4y' + 5y = 0 are Select the correct answer. a. Y1 = e-cos(2x), y2 = eʼsin (2x) b. Y1 = e-*, y2 = e-S* c. Yi= e-*cos(2x), y1=e-* sin(2x) d. Y1 = e-2xcosx, x, y2 = e–2*sinx e. Y1 = e', y2 = 5x
Empty Part only Let L[y]: y"" y'+4xy, yi (x): = sinx, y2(x): =x. Verify that L[y11(x) 4xsinx and to the following differential equations. Ly2 (X)= 4x1. Then use the superposition principle (linearity) to find a solution (a) Lly] 8x sin x - 4x2-1 (b) Lly] 16x+4 -24x sin x y1(x)- cos x tlV]¢»= 4x° Substituting yi (x), y, '(x), and y"(x) into L[y] y""+y' +4xy yields Lfy1(x) 4xsinx. Now verify that +1. Calculate y2'(x) y2'(x) 1 Calculate y2"(x). У2"(х)%3D 0...
Consider differential equation (x - 1)y" – xy' + y = 0. a). Show that yi = el is a solution of this equation. Use the method of reduction of order to find second linearly independent solution y2 of this equation. (2P.) b). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 1. c). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 0. d). Does your answer in b) and c)...
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) =