Q3 of 68 Page 910

Form the differential equation of the family of curves, y=a sin (bx+c), Where a and c are parameters.

Equation of the family of curves, y=a sin (bx+c), Where a and c are parameters.

Differentiating the above equation with respect to x on both sides, we have,


(1)



(Substituting equation 1 in this equation)




This is the required differential equation.


More from this chapter

All 68 →
1

Form the differential equation of the family of straight lines y=mx+c, where m and c are arbitrary constants.

 2

Form the differential equation of the family of concentric circles x2+y2=a2, where a>0 and a is a parameter.

 4

Form the differential equation of the family of curves x=A cos nt+ Bsin nt, where A and B are arbitrary constants.

 5

Form the differential equation of the family of curves y=aebx, where a and b are arbitrary constants.