Advertisements
Advertisements
Question
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
Advertisements
Solution
`("d"y)/("d"x) + y cos x + x = 2 cos x`
This is of the form `("d"y)/("d"x) + "P"y` = Q
Here P = cos x and Q = 2 cos x
`int "Pd"x = int cos x "dx` = sin x
I.F = `"e"^(intpdx)`
= `"e"^(sinx)`
The solution is
y(I.F) = `int "Q" ("I.F") "d"x+ "c"`
yesin x = `int(2 cos x) "e"^(sin x) "d"x`
yesin x = `2int"e"^"t" "dt"`
= 2`"e"^"t" + "c"`
yesin x = `2"e"^(sinx) + "c"`
APPEARS IN
RELATED QUESTIONS
The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x
Solve the following differential equation:
x cos y dy = ex(x log x + 1) dx
Solve the following differential equation:
`2xy"d"x + (x^2 + 2y^2)"d"y` = 0
Choose the correct alternative:
The number of arbitrary constants in the general solutions of order n and n +1are respectively
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) = x + y`
Solve the following:
If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x.
Choose the correct alternative:
If y = ex + c – c3 then its differential equation is
Choose the correct alternative:
The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is
Solve (x2 + y2) dx + 2xy dy = 0
