Form the differential equation of the family of curves `y=asin(b x+c),\ a\ a n d\ c` being parameters.

Explanation

We have given that

`y=asin(b x+c)`

Differentiate with respect to `x` , we get

`dy/dx=abcos(bx+c)`

Again differentiate with respect to `x`

`frac{d^{2} y}{d x^{2}}=-ab^2\sin(bx+c)`

`frac{d^{2} y}{d x^{2}}=-b^2\y`

`frac{d^{2} y}{d x^{2}}+b^2\y=0`

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