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
The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x
Solve: ydx – xdy = 0 dy
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) = x + y`
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
Solve the following:
`("d"y)/("d"x) + y/x = x'e"^x`
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q 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
Solve `x ("d"y)/(d"x) + 2y = x^4`
