Advertisements
Advertisements
Question
Solve the following differential equation:
`(ydx - xdy) cot (x/y)` = ny2 dx
Advertisements
Solution
`(ydx - xdy) cot (x/y)` = ny2 dx
Dividing throughout by 'y2'
`((ydx - xdy)/y^2) cot (x/y)` = n dx
`"d"(x/y)* cot(x/y)` = n dx
`int cot(x/y)* "d"(x/y) = "n" int "d"x`
`log sin(x/y)` = nx + c
`sin(x/y) = "e"^("n"x + "c")`
APPEARS IN
RELATED QUESTIONS
If F is the constant force generated by the motor of an automobile of mass M, its velocity V is given by `"M""dv"/"dt"` = F – kV, where k is a constant. Express V in terms of t given that V = 0 when t = 0
The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x
Solve the following differential equation:
`y"d"x + (1 + x^2)tan^-1x "d"y`= 0
Solve the following differential equation:
(ey + 1)cos x dx + ey sin x dy = 0
Solve the following differential equation:
`("d"y)/("d"x) = tan^2(x + y)`
Solve the following differential equation:
`x ("d"y)/("d"x) = y - xcos^2(y/x)`
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Choose the correct alternative:
The number of arbitrary constants in the particular solution of a differential equation of third order is
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Find the curve whose gradient at any point P(x, y) on it is `(x - "a")/(y - "b")` and which passes through the origin
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) = x + y`
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is
Choose the correct alternative:
The differential equation of x2 + y2 = a2
Choose the correct alternative:
The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is
Solve `x ("d"y)/(d"x) + 2y = x^4`
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
