If y=asin(5x+c), then
dydx=5y
dydx=-5y
d2ydx2=-25y
d2ydx2=25y
Explanation for the correct option.
Step 1. Find the value of dydx.
Differentiate the function y=asin(5x+c) with respect to x.
dydx=ddxasin5x+c=acos5x+c×5[∵ddxsinx=cosx]=5acos5x+c
Step 2. Find the value of d2ydx2.
Differentiate the function dydx=5acos5x+c with respect to x.
d2ydx2=ddx5acos5x+c=5a-sin5x+c×5[∵ddxcosx=-sinx]=-25asin5x+c=-25yy=asin5x+c
Hence, the correct option is C.