Advertisements
Advertisements
Question
Solve: (1 – x) dy – (1 + y) dx = 0
Advertisements
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:
`y"d"x + (1 + x^2)tan^-1x "d"y`= 0
Solve the following differential equation:
`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`
Solve the following differential equation:
`(ydx - xdy) cot (x/y)` = ny2 dx
Solve the following differential equation:
x cos y dy = ex(x log x + 1) dx
Solve the following differential equation:
`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)`
Solve the following differential equation:
`(x^3 + y^3)"d"y - x^2 y"d"x` = 0
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve the following differential equation:
`(1 + 3"e"^(y/x))"d"y + 3"e"^(y/x)(1 - y/x)"d"x` = 0, given that y = 0 when x = 1
Solve: `log(("d"y)/("d"x))` = ax + by
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
