Advertisements
Advertisements
Question
Solve the differential equation `(tan^(-1) x- y) dx = (1 + x^2) dy`
Solution
APPEARS IN
RELATED QUESTIONS
Find the the differential equation for all the straight lines, which are at a unit distance from the origin.
For the differential equation, find the general solution:
`dy/dx + (sec x) y = tan x (0 <= x < pi/2)`
For the differential equation given, find a particular solution satisfying the given condition:
`dy/dx - 3ycotx = sin 2x; y = 2` when `x = pi/2`
Find the equation of the curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.
Solve the differential equation `x dy/dx + y = x cos x + sin x`, given that y = 1 when `x = pi/2`
\[\frac{dy}{dx}\] + y cos x = sin x cos x
Solve the differential equation \[\left( y + 3 x^2 \right)\frac{dx}{dy} = x\]
Solve the following differential equation:- \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\]
Solve the following differential equation: \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\] .
Solve the differential equation: (1 +x2 ) dy + 2xy dx = cot x dx
If f(x) = x + 1, find `"d"/"dx"("fof") ("x")`
Solve the following differential equation:
`"dy"/"dx" + "y"/"x" = "x"^3 - 3`
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:
`"x" "dy"/"dx" + "2y" = "x"^2 * log "x"`
Solve the following differential equation dr + (2r cot θ + sin 2θ) dθ = 0.
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 `(dy)/(dx) + y` = e–x is ______.
The integrating factor of the differential equation sin y `("dy"/"dx")` = cos y(1 - x cos y) is ______.
The integrating factor of the differential equation (1 + x2)dt = (tan-1 x - t)dx is ______.
Which of the following is a second order differential equation?
Integrating factor of the differential equation `(1 - x^2) ("d"y)/("d"x) - xy` = 1 is ______.
The equation x2 + yx2 + x + y = 0 represents
The integrating factor of differential equation `(1 - y)^2 (dx)/(dy) + yx = ay(-1 < y < 1)`
State whether the following statement is true or false.
The integrating factor of the differential equation `(dy)/(dx) + y/x` = x3 is – x.
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 the tangent to the curve x = sin θ and y = cos 2θ at θ = `π/6` is ______.
