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Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constants. Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constants.
Welcome to AskiitiansGiven,y = a sin (x + b) … (1)Differentiating both sides of equation (1) with respect to x,dy/dx = a cos (x + b) … (2)Differentiating again on both sides with respect to x,d2y/dx2= – a sin (x + b) … (3)Eliminating a and b from equations (1), (2) and (3),d2y/ dx2+ y = 0 … (4)The above equation is free from the arbitrary constants a and b.This the required differential equation.Thanks
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