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
Advertisements
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
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`
The solution of the differential equation dy/dx = sec x – y tan x is:
(A) y sec x = tan x + c
(B) y sec x + tan x = c
(C) sec x = y tan x + c
(D) sec x + y tan x = c
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
If y = P eax + Q ebx, show that
`(d^y)/(dx^2)=(a+b)dy/dx+aby=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 the general solution of the differential equation `dy/dx + sqrt((1-y^2)/(1-x^2)) = 0.`
Show that the general solution of the differential equation `dy/dx + (y^2 + y +1)/(x^2 + x + 1) = 0` is given by (x + y + 1) = A (1 - x - y - 2xy), where A is parameter.
If y = etan x+ (log x)tan x then find dy/dx
The solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x} + \frac{\phi\left( \frac{y}{x} \right)}{\phi'\left( \frac{y}{x} \right)}\] is
(x + y − 1) dy = (x + y) dx
(1 + y + x2 y) dx + (x + x3) dy = 0
(x3 − 2y3) dx + 3x2 y dy = 0
\[y - x\frac{dy}{dx} = b\left( 1 + x^2 \frac{dy}{dx} \right)\]
\[\frac{dy}{dx} + 5y = \cos 4x\]
`x cos x(dy)/(dx)+y(x sin x + cos x)=1`
`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \left( \sec x \right) y = \tan x\]
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.
x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.
Form the differential equation having y = (sin–1x)2 + Acos–1x + B, where A and B are arbitrary constants, as its general solution.
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
The general solution of ex cosy dx – ex siny dy = 0 is ______.
The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.
y = aemx+ be–mx satisfies which of the following differential equation?
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
The differential equation for which y = acosx + bsinx is a solution, is ______.
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.
Find the general solution of the differential equation:
`log((dy)/(dx)) = ax + by`.
Solve the differential equation:
`(xdy - ydx) ysin(y/x) = (ydx + xdy) xcos(y/x)`.
Find the particular solution satisfying the condition that y = π when x = 1.
