Question

(b) If
y = sin x + sin x + sin x +
to oo
show that
COS X
dy
dx
2y -1​

Answer 1

y=l^x sinx --------> 1

differentiate 1 to get dy/dx

dy/dx=l^x sinx + l^x cosx ---------> 2

differentiate 2 to get d^2y/dx^2

d^2y/dx^2=l^x sinx + l^x cosx + l^x/cosx-l^x sinx

d^2y/dx^2=2l^x cosx ------------> 3

now put values in equation

d^2y/dx^2 - 2 dy/dx + 2y

2l^x cosx - 2[l^x sinx + l^x cosx] + 2l^x sinx

2l^x cosx - 2l^x sinx - 2l^x cosx + 2l^x sinx

=0

hope this answer will help u