Higher Engineering Mathematics, Sixth Edition

298 Higher Engineering Mathematics

5. Evaluatef′′(θ )whenθ=0given
   f(θ )=2sec3θ. [18]


6. Show that the differential equation
   d^2 y
   dx^2

− 4

dy

dx

+ 4 y=0 is satisfied

wheny=xe^2 x.

7. Show that, if P and Q are constants and
   y=Pcos(lnt)+Qsin(lnt), then

t^2

d^2 y

dt^2

+t

dy

dt

+y= 0