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
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:
`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`
Solve the following differential equation:
`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`
Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Choose the correct alternative:
If y = ex + c – c3 then its differential equation is
Choose the correct alternative:
The differential equation of x2 + y2 = a2
Form the differential equation having for its general solution y = ax2 + bx
Solve (D2 – 3D + 2)y = e4x given y = 0 when x = 0 and x = 1
