298 Higher Engineering Mathematics
5. Evaluate f (θ) when θ = 0 given
f (θ) = 2 sec3θ.
[18]
6. Show that the differential equation
d 2 y
dx 2 − 4
dy
dx
+ 4y = 0 is satisfied
when y = xe 2x .
7. Show that, if P and Q are constants and
y = P cos(ln t ) +Q sin(ln t ), then
t
2 d 2 y
dt 2 + t
d y
dt
+ y = 0
5. Evaluate f (θ) when θ = 0 given
f (θ) = 2 sec3θ.
[18]
6. Show that the differential equation
d 2 y
dx 2 − 4
dy
dx
+ 4y = 0 is satisfied
when y = xe 2x .
7. Show that, if P and Q are constants and
y = P cos(ln t ) +Q sin(ln t ), then
t
2 d 2 y
dt 2 + t
d y
dt
+ y = 0