Verify that yi = XpJp(x) and y, = xryp(x) are linearly independent solutions of xy" + (1-2p)y, + ...
4. Verify that yi xPJp(x) and y2 - xPYp(x) are linearly independent solutions of xy" + (1-2 )y, + xy-0, x > 0.
4. Verify that yi xPJp(x) and y2 - xPYp(x) are linearly independent solutions of xy" + (1-2 )y, + xy-0, x > 0.
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.)
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)...
ra17070309238key 7RyEosqso4T Mat int) Find two linearly independent solutions of 2x2y"-xy' + (-6x + 1)y--0, z > 0 of the form where ri T2 Enter T2 b2
ra17070309238key 7RyEosqso4T Mat int) Find two linearly independent solutions of 2x2y"-xy' + (-6x + 1)y--0, z > 0 of the form where ri T2 Enter T2 b2
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
(Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independent solutions of 3. хзу",-z?y"-2xy' + 6y-0 on (-oo, 0) and (0, +00). Write down the general solution to (4 (b) Find a fundamental set S of solutions of
(Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independent solutions of 3. хзу",-z?y"-2xy' + 6y-0 on (-oo, 0) and (0, +00). Write down the general...
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
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
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) =