Question

If , prove that

Answer 1

Let, y=5cosx−sin3x.

The first order derivative is obtained by differentiating the function with respect to x.

dy dx = d( 5cosx−3sinx ) dx = d dx ( 5cosx )− d dx ( 3sinx ) =5 d dx ( cosx )−3 d dx ( sinx ) =−5sinx−3cosx

Again differentiate the above function with respect to x.

d dx ( dy dx )= d dx [ −5sinx−3cosx ] d 2 y d x 2 =− d dx [ 5sinx+3cosx ] =−[ 5cosx−3sinx ] =−y

Further simplify the above function.

d 2 y d x 2 =−y d 2 y d x 2 +y=0

Hence, the given condition d 2 y d x 2 +y=0 is proved.