Advertisements
Advertisements
Question
Solve the following differential equation:
`("d"^2y)/("d"x^2) + 16y = 0`
Advertisements
Solution
Given (D2 + 16) y =0
The auxiliary equation is m2 + 16 = 0
⇒ m2 = – 16
⇒ m = ± 4i
It is of the form α ± iβ, α = 0, β = 4
The complementary function (C.F) is e0x [A cos 4x + B sin 4x]
The general solution is y = [A cos 4x + B sin 4x]
APPEARS IN
RELATED QUESTIONS
Solve the following differential equation:
`("d"^2y)/("d"x^2) - 6 ("d"y)/("d"x) + 8y = 0`
Solve the following differential equation:
`("d"^2y)/("d"x^2) - 4("d"y)/("d"x) + 4y = 0`
Solve the following differential equation:
(D2 + 2D + 3)y = 0
Solve the following differential equation:
(D2 – 2D – 15)y = 0 given that `("d"y)/("d"x)` = 0 and `("d"^2y)/("d"x^2)` = 2 when x = 0
Solve the following differential equation:
(D2 – 3D + 2)y = e3x which shall vanish for x = 0 and for x = log 2
Solve the following differential equation:
(D2 + D – 2)y = e3x + e–3x
Solve the following differential equation:
(D2 – 10D + 25) y = 4e5x + 5
Solve the following differential equation:
Suppose that the quantity demanded Qd = `13 - 6"p" + 2 "dp"/"dt" + ("d"^2"p")/("dt"^2)` and quantity supplied Qs = `- 3 + 2"p"` where p is the price. Find the equilibrium price for market clearance
Choose the correct alternative:
The integrating factor of `x ("d"y)/("d"x) - y = x^2` is
Choose the correct alternative:
The P.I of (3D2 + D – 14)y = 13e2x is
