Q5 of 462 Page 22

Form the differential equation of the family of curves,

x = A cos nt + B sin nt, where A and B are arbitrary constant.

As the given equation has two different arbitrary constants so we can differentiate it twice with respect to x.

x = A cos nt + B sin nt


On differentiating with respect to t we get,



Again, differentiating with respect to x,




As x = A cos nt + B sin nt




Hence, is the required differential equation.


More from this chapter

All 462 →
3

Form the differential equation from the following primitives where constants are arbitrary:

y = ax2 + bx + c

 4

Form the differential equation of the family of curves y = Ae2x + Be–2x, where A and B are arbitrary constants.

 6

Form the differential equation corresponding to y2 = a(b – x2) by eliminating a and b.

 7

Form the differential equation corresponding to y2 – 2 ay + x2 = a2 by eliminating a.