Advertisements
Advertisements
प्रश्न
Solve:
`1 + (dy)/(dx) = cosec (x + y)`; put x + y = u.
Advertisements
उत्तर
`1 + dy/dx = cosec (x + y)` ...(i)
Put x + y = u
⇒ `1 + dy/dx = du/dx`
∴ 1 + `"dy"/("d"x)="du"/("d"x)`
Given differential equation (i) becomes
`(du)/dx` = cosec u
∴ `(du)/("cosec" u) = dx`
`therefore int 1/("cosec" u) du = int dx`
∴ ∫sin u du = ∫dx
∴ −cos u = x + c
∴ x + cos u + c = 0
∴ x + cos (x + y) + c = 0 ...(∵ x + y = u)
APPEARS IN
संबंधित प्रश्न
If y = sec x + xlogx, then `"dy"/"dx"` is
`"d"/"dx"`[cos (3x + 2)] = ?
The differential equation whose solution is y = Aex + Be-x, is
The solution of the differential equation `1 + "dy"/"dx" = (sin^2(x + y))/(cos (x + y))` is
The particular solution of the differential equation `"y"("dx"/"dy")` = x log x at x = e and y = 1 is ______.
The integrating factor of the differential equation x`"dy"/"dx"` + y log x = x2 is ______.
The general solution of the differential equation (1 + y2) + `(x - e^(tan^-1 y)) "dy"/"dx"` = 0 is.
Solution of differential equation `xdy/dx - y = x^3` is ______
The solution of the differential equation `dy/dx = (x - 2y + 1)/(2(x - 2y))` is ______
The solution of the differential equation `(y^2 + xy^2)dx/dy + x^2 - yx^2 = 0` is ______
Solution of the equation `dy/dx + y/(x + logy) = 0` is ______
A solution of the equation tan-1(1 + x) + tan-1(1 - x) = `pi/2` is ______
The solution of the differential equation y dx - x dy = xy dx is ______.
The solution of the equation `dx/dy - x = y + 1` is ______
The solution of differential equation `(x^2 + 1) "dy"/"dx" + (y^2 + 1) = 0` is ______.
The solution of the differential equation `dy/dx + y/x = 1 - x^3 + 4x` is ______
Particular solution of differential equation `e^{dy/dx} = x:y(1) = 3; x > 0` is ______
Solution of `sinx dy/dx + y cosx = 1` is ______
The solution of the differential equation x(ey - 1)dy + (x3 - 1)ey dx = 0 is ______.
The solution of the differential equation `dy/dx=1+y/x+(y/x)^2` is ______.
The solution of the differential equation `dy/dx - cos^2y = 0` is ______
Solution of the differential equation `dy/dx = ((tanx - y))/(cos^2x)` is ______
The solution of the differential equation `dy/dx = x^3 + cos4x` is ______
The solution of the differential equation `("d"y)/("d"x) + 2y tan x = 2x cos^2x` is ______.
The solution of the equation `1 + ("d"x)/("d"y) = (2y)/x` is ______.
The solution for the differential equation `("d"y)/y +("d"x)/x` = 0 is ______.
The general solution of differential equation `dx/dy` = cos (x + y) is ______.
The particular solution of the differential equation x dy + 2y dx = 0, when x = 2,y = 1 is ______.
The particular solution of the differential equation `y(1 + log x) dx/dy - x log x = 0`, when x = e, y = e2 is ______.
Find the particular solution of the differential equation `dy/dx` = e2y cos x, when x = `π/6`, y = 0
Verify that y sec x = tan x + c is a solution of the differential equation `dy/dx + y tan x` = sec x.
Solution of the differential equation `dy/dx = (xy^2 + x)/(x^2y + y)` is ______.
Find the general solution of the differential equation `tan y * dy/dx = sin(x + y) - sin(x - y)`.
Solution of the differential equation `(x + y dy/dx)(x^2 + y^2)` = 1, is ______.
