Advertisements
Advertisements
प्रश्न
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
पर्याय
tanx + tany = k
tanx – tany = k
`tanx/tany` = k
tanx . tany = k
Advertisements
उत्तर
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is tanx . tany = k.
Explanation:
The given differential equation is tan y sec2x dx + tan x sec2y dy = 0
⇒ tan x sec2y dy = – tan y sec2x dx
⇒ `(sec^2y)/tany * "d"y = (-sec^2x)/tanx * "d"x`
Integrating both sides, we get
⇒ `int (sec^2y)/tany "d"y = int (-sec^2x)/tanx "d"x`
⇒ `log |tan y| = - log |tan x| + log "c"`
⇒ `log |tan y| + log |tan x| = log "c"`
APPEARS IN
संबंधित प्रश्न
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`
The differential equation of the family of curves y=c1ex+c2e-x is......
(a)`(d^2y)/dx^2+y=0`
(b)`(d^2y)/dx^2-y=0`
(c)`(d^2y)/dx^2+1=0`
(d)`(d^2y)/dx^2-1=0`
If x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Solve the differential equation `dy/dx -y =e^x`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = Ax : xy′ = y (x ≠ 0)
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y – cos y = x : (y sin y + cos y + x) y′ = y
The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.
The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is
The solution of x2 + y2 \[\frac{dy}{dx}\]= 4, is
The solution of the differential equation \[\frac{dy}{dx} - ky = 0, y\left( 0 \right) = 1\] approaches to zero when x → ∞, if
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
\[\frac{dy}{dx} + 5y = \cos 4x\]
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
`2 cos x(dy)/(dx)+4y sin x = sin 2x," given that "y = 0" when "x = pi/3.`
For the following differential equation, find a particular solution satisfying the given condition:- \[\cos\left( \frac{dy}{dx} \right) = a, y = 1\text{ when }x = 0\]
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx, x ≠ 0.
Solve the differential equation: `(d"y")/(d"x") - (2"x")/(1+"x"^2) "y" = "x"^2 + 2`
Find the differential equation of all non-horizontal lines in a plane.
The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
If y(t) is a solution of `(1 + "t")"dy"/"dt" - "t"y` = 1 and y(0) = – 1, then show that y(1) = `-1/2`.
Solution of differential equation xdy – ydx = 0 represents : ______.
Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.
The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
General solution of `("d"y)/("d"x) + ytanx = secx` is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
The solution of `("d"y)/("d"x) = (y/x)^(1/3)` is `y^(2/3) - x^(2/3)` = c.
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
