Advertisements
Advertisements
प्रश्न
Solve the differential equation:
cosec3 x dy − cosec y dx = 0
उत्तर
Given, differential equation is
cosec3 x dy − cosec y dx = 0
⇒ cosec3 x dy = cosec y dx
⇒ `int "dy"/("cosec y") = int "dx"/("cosec"^3 "x")`
⇒ `int sin "y dy" = int sin^3 "x dx"`
⇒ `- cos "y" = int sin^2 "x". sin "x dx"`
= `int (1 - cos^2 "x"). sin "x dx"`
Let cos x = t,
⇒ − sin x dx = dt
∴ − cos y = `- int (1 - "t"^2) "dt"`
⇒ cos y = `"t" - "t"^3/3 + "c"`
∴ cos y = `cos "x" - (cos^3 "x")/3 + "c"`
APPEARS IN
संबंधित प्रश्न
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
`x/a + y/b = 1`
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = e2x (a + bx)
Solve the differential equation `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`
The general solution of a differential equation of the type `dx/dy + P_1 x = Q_1` is ______.
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.
Find the differential equation of all the circles which pass through the origin and whose centres lie on x-axis.
Form the differential equation having \[y = \left( \sin^{- 1} x \right)^2 + A \cos^{- 1} x + B\], where A and B are arbitrary constants, as its general solution.
The equation of the curve satisfying the differential equation y (x + y3) dx = x (y3 − x) dy and passing through the point (1, 1) is
Verify that xy = a ex + b e−x + x2 is a solution of the differential equation \[x\frac{d^2 y}{d x^2} + 2\frac{dy}{dx} - xy + x^2 - 2 = 0.\]
Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]
Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} + 4x = e^x\]
\[\frac{dy}{dx} = x^2 e^x\]
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
tan y dx + tan x dy = 0
cos y log (sec x + tan x) dx = cos x log (sec y + tan y) dy
(1 − x2) dy + xy dx = xy2 dx
Find the general solution of the differential equation `"dy"/"dx" = y/x`.
The general solution of the differential equation `(dy)/(dx) + x/y` = 0 is
The general solution of the differential equation `(dy)/(dx) = e^(x + y)` is
The general solution of the differential equation of the type `(dx)/(dy) + p_1y = theta_1` is
The general solution of the differential equation `(ydx - xdy)/y` = 0
What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2) (-2 < y < 2)`
The general solution of the differential equation y dx – x dy = 0 is ______.
