Advertisements
Advertisements
प्रश्न
(1 + y + x2 y) dx + (x + x3) dy = 0
Advertisements
उत्तर
\[\left( 1 + y + x^2 y \right)dx + \left( x + x^3 \right)dy = 0\]
\[ \Rightarrow dx + y\left( 1 + x^2 \right)dx + x\left( 1 + x^2 \right)dy = 0\]
\[ \Rightarrow dx + \left( 1 + x^2 \right) \left[ ydx + xdy \right] = 0\]
\[ \Rightarrow \left( 1 + x^2 \right) \left[ ydx + xdy \right] = - dx\]
\[ \Rightarrow \left[ ydx + xdy \right] = - \frac{1}{\left( 1 + x^2 \right)}dx\]
\[ \Rightarrow \left[ ydx + xdy \right] = - \frac{dx}{\left( 1 + x^2 \right)}\]
On integrating both side we get,
\[\left( xy \right) = - \int\frac{1}{1 + x^2}dx\]
\[ \Rightarrow xy = - \tan^{- 1} x + c\]
\[ \Rightarrow xy + \tan^{- 1} x = c\]
APPEARS IN
संबंधित प्रश्न
Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0.
If x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`
Solve the differential equation `dy/dx=(y+sqrt(x^2+y^2))/x`
Find the particular solution of the differential equation `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0
Find the particular solution of the differential equation `dy/dx=(xy)/(x^2+y^2)` given that y = 1, when x = 0.
The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`
Find the particular solution of the differential equation
`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The solution of the differential equation x dx + y dy = x2 y dy − y2 x dx, is
Which of the following differential equations has y = x as one of its particular solution?
The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that
\[\frac{dy}{dx} = \frac{\sin x + x \cos x}{y\left( 2 \log y + 1 \right)}\]
\[\frac{dy}{dx} = \left( x + y \right)^2\]
(x + y − 1) dy = (x + y) dx
(x2 + 1) dy + (2y − 1) dx = 0
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sin^{- 1} x\]
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Solve the following differential equation:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
Find the equation of a curve passing through the point (−2, 3), given that the slope of the tangent to the curve at any point (x, y) is `(2x)/y^2.`
Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x-coordinate and the product of the x-coordinate and y-coordinate of that point.
Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0 "given that" "y" = 0 "when" "x" = 1`.
Find the general solution of `(x + 2y^3) "dy"/"dx"` = y
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
Solution of differential equation xdy – ydx = 0 represents : ______.
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
The solution of the differential equation `("d"y)/("d"x) + (2xy)/(1 + x^2) = 1/(1 + x^2)^2` is ______.
The solution of the differential equation ydx + (x + xy)dy = 0 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:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
