Advertisements
Advertisements
प्रश्न
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
उत्तर
Given differential equation is `(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
⇒ `(dy)/(dx) = (3e^(2x)(1 + e^(2x)))/(e^x + 1/e^x)`
⇒ `(dy)/(dx) = (3e^(2x)(1 + e^(2x)))/((e^(2x) + 1)) xx e^x`
⇒ `(dy)/(dx)` = 3e3x
⇒ dy = 3e3xdx
Integrating both sides, we get
`intdy = 3inte^(3x)dx`
⇒ y = `3 e^(3x)/3 + C`
y = `e^(3x) + C`
APPEARS IN
संबंधित प्रश्न
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`
If x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`
Solve the differential equation `dy/dx=(y+sqrt(x^2+y^2))/x`
Find the particular solution of the differential equation `dy/dx=(xy)/(x^2+y^2)` given that y = 1, when x = 0.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y = sqrt(a^2 - x^2 ) x in (-a,a) : x + y dy/dx = 0(y != 0)`
If y = etan x+ (log x)tan x then find dy/dx
if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`
Solve the differential equation:
`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1
The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
The solution of the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 0, is
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
\[\frac{dy}{dx} - y \tan x = - 2 \sin x\]
`2 cos x(dy)/(dx)+4y sin x = sin 2x," given that "y = 0" when "x = pi/3.`
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]
Find the differential equation of all non-horizontal lines in a plane.
The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.
Find the general solution of `(x + 2y^3) "dy"/"dx"` = y
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
General solution of `("d"y)/("d"x) + y` = sinx is ______.
The member of arbitrary constants in the particulars solution of a differential equation of third order as
Which of the following differential equations has `y = x` as one of its particular solution?
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
