Q52 of 96 Page 12

If , prove that

Formula: –








Given: –


y = xn(acos(logx) + bsin(logx))


y = axncos(logx) + bxnsin(logx)







= xn (na + b)[(n – 1) cos(logx) – sin (logx) ] + (bn – a) xn [(n – 1) sin(logx) + cos(logx)] + (1 – 2n)xn – 1cos(logx)(na + b) + (1 – 2n)xn – 1sin(logx)(bn – a) + a(1 + n2)xncos(logx) + bxn(1 + n2)sin(logx)



More from this chapter

All 96 →
50

Find A and B so that y = A sin 3x + Bcos 3x satisfies the equation

 51

If y = A e – kt cos (pt + c), prove that , where n2 = p2 + k2.

 53

If y = a {x + √x2 + 1}n + b{x – √x2 + 1} – n, prove that (x2 – 1) .

 1

Find the second order derivatives of each of the following functions:

x3 + tan x