Advertisements
Advertisements
प्रश्न
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Advertisements
उत्तर
`y(1 - x) - x ("d"y)/("d"x)` = 0
`y(1 - x) = x ("d"y)/("d"x)`
⇒ `((1 - x))/x "d"x = 1/y "d"y`
`(1/x - x/x) "d"x = 1/y "d"y`
⇒ `(1/x - 1) "d"x = 1/y "d"y`
Integrating on both sides
`int (1/x - 1) "d"x = int 1/y "d"y`
`log x - x = log y + "c"`
APPEARS IN
संबंधित प्रश्न
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:
(ey + 1)cos x dx + ey sin x dy = 0
Solve: (1 – x) dy – (1 + y) dx = 0
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Solve the following:
`("d"y)/(""dx) + y cos x = sin x cos x`
Solve the following:
If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x.
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) + "P"y` = Q where P and Q are the function of x is
Choose the correct alternative:
A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution
Solve `x ("d"y)/(d"x) + 2y = x^4`
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
