Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
`y"d"x + (1 + x^2)tan^-1x "d"y`= 0
Advertisements
उत्तर
`y"d"x + (1 + x^2)tan^-1x "d"y`
Take t = tan–1x
dt `1/(1 + x^2) "d"x`
The equation can be written as
`("d"x)/((1 + x^2)tan^-) = - ("d"y)/y`
`"dt"/"t" = - ("d"y)/y`
Taking Integration on both sides, we get
`int "dt"/"t" = int ("d"y)/y`
log t = – log y + log C
log(tan–1x) = – log y + log C
log (y(tan–1x)) + log y = log C
y tan–1x = 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 the following differential equation:
(ey + 1)cos x dx + ey sin x dy = 0
Solve the following differential equation:
`("d"y)/("d"x) = tan^2(x + y)`
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve the following differential equation:
(x2 + y2) dy = xy dx. It is given that y (1) = y(x0) = e. Find the value of x0
Choose the correct alternative:
The solution of `("d"y)/("d"x) + "p"(x)y = 0` is
Choose the correct alternative:
The solution of `("d"y)/("d"x) = 2^(y - x)` is
Solve: ydx – xdy = 0 dy
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
(y2 – 2xy) dx = (x2 – 2xy) dy
Solve the following:
`x ("d"y)/("d"x) + 2y = x^4`
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
Solve the following:
A bank pays interest by continuous compounding, that is by treating the interest rate as the instantaneous rate of change of principal. A man invests ₹ 1,00,000 in the bank deposit which accrues interest, 8% per year compounded continuously. How much will he get after 10 years? (e0.8 = 2.2255)
Choose the correct alternative:
The differential equation of y = mx + c is (m and c are arbitrary constants)
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"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
Solve `("d"y)/("d"x) = xy + x + y + 1`
