Advertisements
Advertisements
प्रश्न
Solve: `log(("d"y)/("d"x))` = ax + by
Advertisements
उत्तर
`log(("d"y)/("d"x))` = ax + by
`(("d"y)/("d"x)) = "e"^("a"x + "b"y)`
`("d"y)/("d"x) = "e"^("a"x)* "e"^("b"y)`
⇒ `("d"y)/"e"^("b"y) = "e"^("a"x) "d"x`
⇒ `"e"^("a"x) "d"x = "e"^(-"b"y) "d"y`
Integrating on both sides
`int "e"^("a"x) "d"x = int "e"^(-"b"y) "d"y`
`"e"^("a"x)/"a" = "e"^(-"b"y)/(-"b") + "c"`
APPEARS IN
संबंधित प्रश्न
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
Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)
Solve the following differential equation:
`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0
Solve the following differential equation:
`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)`
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Solve: ydx – xdy = 0 dy
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is
Choose the correct alternative:
If sec2 x is an integrating factor of the differential equation `("d"y)/("d"x) + "P"y` = Q then P =
A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ’m’ of intervals between overhauls by the equation `"m"^2 "dC"/"dm" + 2"mC"` = 2 and c = 4 and when = 2. Find the relationship between C and m
