Advertisements
Advertisements
प्रश्न
Solve the differential equation `(tan^(-1) x- y) dx = (1 + x^2) dy`
उत्तर
APPEARS IN
संबंधित प्रश्न
For the differential equation, find the general solution:
`dy/dx + (sec x) y = tan x (0 <= x < pi/2)`
For the differential equation, find the general solution:
`(x + y) dy/dx = 1`
For the differential equation given, find a particular solution satisfying the given condition:
`dy/dx + 2y tan x = sin x; y = 0 " when x " = pi/3`
For the differential equation given, find a particular solution satisfying the given condition:
`(1 + x^2)dy/dx + 2xy = 1/(1 + x^2); y = 0` when x = 1
The Integrating Factor of the differential equation `dy/dx - y = 2x^2` is ______.
The integrating factor of the differential equation.
`(1 - y^2) dx/dy + yx = ay(-1 < y < 1)` is ______.
The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?
(x + tan y) dy = sin 2y dx
Solve the following differential equation:- \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\]
Solve the following differential equation:-
\[\left( 1 + x^2 \right)\frac{dy}{dx} - 2xy = \left( x^2 + 2 \right)\left( x^2 + 1 \right)\]
Find the integerating factor of the differential equation `xdy/dx - 2y = 2x^2` .
If f(x) = x + 1, find `"d"/"dx"("fof") ("x")`
Solve the differential equation: `(1 + x^2) dy/dx + 2xy - 4x^2 = 0,` subject to the initial condition y(0) = 0.
Solve the following differential equation:
`cos^2 "x" * "dy"/"dx" + "y" = tan "x"`
Solve the following differential equation:
`("x" + 2"y"^3) "dy"/"dx" = "y"`
Solve the following differential equation:
`"dy"/"dx" + "y" * sec "x" = tan "x"`
Solve the following differential equation dr + (2r cot θ + sin 2θ) dθ = 0.
Solve the following differential equation:
y dx + (x - y2) dy = 0
Find the equation of the curve passing through the point `(3/sqrt2, sqrt2)` having a slope of the tangent to the curve at any point (x, y) is -`"4x"/"9y"`.
The curve passes through the point (0, 2). The sum of the coordinates of any point on the curve exceeds the slope of the tangent to the curve at any point by 5. Find the equation of the curve.
The integrating factor of the differential equation `x (dy)/(dx) - y = 2x^2` is
The integrating factor of differential equation `(1 - y)^2 (dx)/(dy) + yx = ay(-1 < y < 1)`
Let y = y(x) be a solution curve of the differential equation (y + 1)tan2xdx + tanxdy + ydx = 0, `x∈(0, π/2)`. If `lim_(x→0^+)` xy(x) = 1, then the value of `y(π/2)` is ______.
The slope of tangent at any point on the curve is 3. lf the curve passes through (1, 1), then the equation of curve is ______.