Advertisements
Advertisements
प्रश्न
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.
विकल्प
`sinx/siny` = c
sinx siny = c
sinx + siny = c
cosx cosy = c
उत्तर
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is sinx siny = c.
Explanation:
The given differential equation is cosx siny dx + sinx cosy dy = 0
⇒ sinx cosy dy = – cosx siny dx
⇒ `cosy/siny "d"y = - cosx/sinx "d"x`
⇒ coty dy = – cotx dx
Integrating both sides, we have
⇒ `int coty "d"y = - int cot x "d"x`
⇒ `log|sin y| = - log|sin| + log"c"`
⇒ `log|siny| + log|sinx| = log"c"`
⇒ `log|siny . sin x| = log"c"`
⇒ sinx siny = c
APPEARS IN
संबंधित प्रश्न
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = cos x + C : y′ + sin x = 0
Find a particular solution of the differential equation `dy/dx + y cot x = 4xcosec x(x != 0)`, given that y = 0 when `x = pi/2.`
The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then
The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is
The solution of the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + 1 + y^2 = 0\], is
Find the particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.
\[\frac{dy}{dx} + 1 = e^{x + y}\]
\[\frac{dy}{dx} = \frac{y\left( x - y \right)}{x\left( x + y \right)}\]
\[\frac{dy}{dx} + 5y = \cos 4x\]
`x cos x(dy)/(dx)+y(x sin x + cos x)=1`
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \left( 1 + x^2 \right)\left( 1 + y^2 \right)\]
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.
The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = 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`.
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
Which of the following is the general solution of `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + y` = 0?
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
Find a particular solution, satisfying the condition `(dy)/(dx) = y tan x ; y = 1` when `x = 0`
Find the general solution of the differential equation:
`log((dy)/(dx)) = ax + by`.
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
