Advertisements
Advertisements
प्रश्न
Solve `x ("d"y)/(d"x) + 2y = x^4`
उत्तर
`x ("d"y)/(d"x) + 2y = x^4`
÷ each term by x
`("d"y)/("d"x) + (2y)/x = x^2`
This is of the form `("d"y)/("d"x) + "P"y` = Q
Here P = `2/x` and Q = x3
`int "Pd"x = 2int1/x "d"x`
= 2 log x
= log x2
I.F = `"e"^(intpdx)`
=`"e"^(logx^2)`
= x2
This solution is
y(I.F) = `int "Q"x ("I.F") d"x + "c"`
y(x2) = `int (x^3 xx x^2) 'd"x + "c"`
yx2 = `int x^5 "d"x + "c"`
⇒ yx2 = `x^6/6 + "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:
`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve the following differential equation:
`(1 + 3"e"^(y/x))"d"y + 3"e"^(y/x)(1 - y/x)"d"x` = 0, given that y = 0 when x = 1
Choose the correct alternative:
The general solution of the differential equation `log(("d"y)/("d"x)) = x + y` is
Solve: `("d"y)/("d"x) = "ae"^y`
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
Choose the correct alternative:
The differential equation of x2 + y2 = a2
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
