Advertisements
Advertisements
प्रश्न
Solve: (1 – x) dy – (1 + y) dx = 0
Advertisements
उत्तर
(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
संबंधित प्रश्न
Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)
Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`
Solve: `("d"y)/("d"x) = y sin 2x`
Solve: `log(("d"y)/("d"x))` = ax + by
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
Solve the following:
`("d"y)/("d"x) + y/x = x"e"^x`
Choose the correct alternative:
If y = ex + c – c3 then its differential equation is
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 y = mx + c is (m and c are arbitrary constants)
Solve `x ("d"y)/(d"x) + 2y = x^4`
