Advertisements
Advertisements
प्रश्न
Solve the following:
`("d"y)/("d"x) + y/x = x"e"^x`
Advertisements
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
Solve the following differential equation:
`("d"y)/("d"x) = sqrt((1 - y^2)/(1 - x^2)`
Solve the following differential equation:
`x ("d"y)/("d"x) = y - xcos^2(y/x)`
Choose the correct alternative:
The general solution of the differential equation `log(("d"y)/("d"x)) = x + y` is
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
Solve the following:
If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x
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 x2 + y2 = a2
Choose the correct alternative:
A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution
Choose the correct alternative:
A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution
Solve `x ("d"y)/(d"x) + 2y = x^4`
