Advertisements
Advertisements
प्रश्न
Find the general solution of the differential equation \[\frac{dy}{dx} = \frac{x + 1}{2 - y}, y \neq 2\]
Advertisements
उत्तर
We have,
\[\frac{dy}{dx} = \frac{x + 1}{2 - y}\]
\[ \Rightarrow \left( 2 - y \right)dy = \left( x + 1 \right)dx\]
Integrating both sides, we get
\[\int\left( 2 - y \right)dy = \int\left( x + 1 \right)dx\]
\[ \Rightarrow 2y - \frac{y^2}{2} = \frac{x^2}{2} + x + C_1 \]
\[ \Rightarrow \frac{x^2}{2} + x + C_1 - 2y + \frac{y^2}{2} = 0\]
\[ \Rightarrow x^2 + 2x + y^2 + 2 C_1 - 4y = 0\]
\[ \Rightarrow x^2 + y^2 + 2x - 4y + C = 0 ........\left[\text{Where, }C = 2 C_1 \right]\]
APPEARS IN
संबंधित प्रश्न
The differential equation of `y=c/x+c^2` is :
(a)`x^4(dy/dx)^2-xdy/dx=y`
(b)`(d^2y)/dx^2+xdy/dx+y=0`
(c)`x^3(dy/dx)^2+xdy/dx=y`
(d)`(d^2y)/dx^2+dy/dx-y=0`
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`
Find the particular solution of the differential equation `(1+x^2)dy/dx=(e^(mtan^-1 x)-y)` , give that y=1 when x=0.
Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.
Find the particular solution of the differential equation x (1 + y2) dx – y (1 + x2) dy = 0, 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 = cos x + C : y′ + sin x = 0
Solve the differential equation `cos^2 x dy/dx` + y = tan x
Solve the differential equation:
`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1
The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] is
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 x2 + y2 \[\frac{dy}{dx}\]= 4, is
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
\[\frac{dy}{dx} - y \tan x = e^x\]
x2 dy + (x2 − xy + y2) dx = 0
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
y dx + (x − y2) dy = 0
Find a particular solution of the following differential equation:- \[\left( 1 + x^2 \right)\frac{dy}{dx} + 2xy = \frac{1}{1 + x^2}; y = 0,\text{ when }x = 1\]
Find a particular solution of the following differential equation:- x2 dy + (xy + y2) dx = 0; y = 1 when x = 1
Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx, x ≠ 0.
Find the differential equation of all non-horizontal lines in a plane.
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = k.
Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`
tan–1x + tan–1y = c is the general solution of the differential equation ______.
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 ______.
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
General solution of `("d"y)/("d"x) + y` = sinx is ______.
Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.
`(dy)/(dx) + ycotx = 2/(1 + sinx)`
