Find out the differential equation of `y=Acosx^2+Bsinx^2`

Explanation

`y = Acosx^2+Bsinx^2`

`=>dy/dx = A(-sinx^2)(2x)+B(cosx^2)(2x)`

`=>dy/dx = 2x(Bcosx^2 - Asinx^2)`

`=>(d^2y)/dx^2 = 2x(-Bsinx^2(2x) - Acosx^2(2x))+(Bcosx^2 - Asinx^2)(2)`

`=>(d^2y)/dx^2 = -4x^2(Acosx^2+Bsinx^2) +2(Bcosx^2 - Asinx^2)`

`=>(d^2y)/dx^2 = -4x^2y +1/x(dy/dx)`

`=>(d^2y)/dx^2 -1/x(dy/dx) + 4x^2y = 0`, which is the required differential equation.