Advertisements
Advertisements
Question
Solve: (1 – x) dy – (1 + y) dx = 0
Solution
(1 – x) dy = (1 + y) dx
`("d"y)/((1 + y)) = ("d"x)/((1 - x))`
Integrating on both sides
`int ("d"y)/((1 + y)) = int ("d"x)/((1 - x))`
`int ("d"y)/((1 + y)) = - int (- "d"x)/((1 - x))`
`log (1 + y) = - log (1 - x) + log "c"`
`log (1 + y) = log ("c"/((1 - x)))`
⇒ `(1 + y) = "c"/((1 - x))`
∴ `(1 - x)(1 + y)` = c
APPEARS IN
RELATED QUESTIONS
Solve the following differential equation:
`sin ("d"y)/("d"x)` = a, y(0) = 1
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve the following differential equation:
`x ("d"y)/("d"x) = y - xcos^2(y/x)`
Choose the correct alternative:
The solution of `("d"y)/("d"x) + "p"(x)y = 0` is
Choose the correct alternative:
If sin x is the integrating factor of the linear differential equation `("d"y)/("d"x) + "P"y = "Q"`, then P is
Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
Choose the correct alternative:
A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution
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
