Advertisements
Advertisements
प्रश्न
Solve the following:
`("d"y)/("d"x) + y/x = x"e"^x`
उत्तर
It is of the form `("d"y)/("d"x) + "P"y` = Q
Here P = `1/x`
Q = xex
`int "Pd"x = int 1/x "d"x`
= log x
I.F = `"e"^(intpdx)`
= elog x
= x
The required solution is
y(I.F) = `int "Q"("I.F") "d"x + "c"`
y(x) = `int x"e"^x (x) "d"x`
xy = `int x^2"e"^x "d"x`
∴ xy = `x^2"e"^x - 2x"e"^x + 2"e"^x + "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
Solve the following differential equation:
`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0
Solve the following differential equation:
x cos y dy = ex(x log x + 1) dx
Solve: ydx – xdy = 0 dy
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Solve the following:
`x ("d"y)/("d"x) + 2y = x^4`
Solve the following:
`("d"y)/("d"x) + (3x^2)/(1 + x^3) y = (1 + x^2)/(1 + x^3)`
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)
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
