Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
`("d"^2y)/("d"x^2) - 2"k" ("d"y)/("d"x) + "k"^2y = 0`
Advertisements
उत्तर
Given (D2 – 2kD + k2)y = 0
D = `"d"/("d"x)`
The auxiliary equations is m2 – 2km + k = 0
⇒ (m – k)2 = 0
⇒ m = k, k
Roots are real and equal
The complementary function (C.F) is (Ax + B)ekx
The general solution is y = (Ax + B)ekx
APPEARS IN
संबंधित प्रश्न
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:
(4D2 + 4D – 3)y = e2x
Solve the following differential equation:
`("d"^2y)/("d"x^2) + 16y = 0`
Solve the following differential equation:
(3D2 + D – 14)y – 13e2x
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 complementary function of (D2 + 4) y = e2x is
Choose the correct alternative:
The integrating factor of `x ("d"y)/("d"x) - y = x^2` is
Choose the correct alternative:
The complementary function of `("d"^2y)/("d"x^2) - ("d"y)/("d"x) = 0` is
Choose the correct alternative:
The general solution of the differential equation `("d"y)/("d"x) = cos x` is
