Advertisements
Advertisements
प्रश्न
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
Advertisements
उत्तर
`("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
संबंधित प्रश्न
Choose the correct alternative:
The general solution of the differential equation `log(("d"y)/("d"x)) = x + y` is
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Solve: (1 – x) dy – (1 + y) dx = 0
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
Solve the following:
`("d"y)/("d"x) - y/x = x`
Choose the correct alternative:
If y = ex + c – c3 then its differential equation is
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q 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 (D2 – 3D + 2)y = e4x given y = 0 when x = 0 and x = 1
Solve x2ydx – (x3 + y3) dy = 0
