Advertisements
Advertisements
प्रश्न
Solve the following:
`x ("d"y)/("d"x) + 2y = x^4`
उत्तर
The given equation can be reduced to
`("d"y)/("d"x) + (2y)/x = x^3`
It is of the form `("d"y)/("d"x) + "P"y` = Q
Here P = `2/x`, Q = x3
`int "pd"x = int 2/x "d"x`
= `2 int 1/x "d"x`
= `2 log x - log x^2`
I.F = `"e"^(int Pdx)`
= `"e"^(log x^2)`
= x2
The required solution is
y(I.F) = `int "Q" ("I.F") "d"x + "c"`
y(x2) = `int x^3 (x^2) "d"x + "c"`
x2y = `int x^5 "d"x + "c"`
x2y = `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:
(ey + 1)cos x dx + ey sin x dy = 0
Solve the following differential equation:
`("d"y)/("d"x) = tan^2(x + y)`
Solve: ydx – xdy = 0 dy
Solve: (1 – x) dy – (1 + y) dx = 0
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)`
Choose the correct alternative:
The differential equation of y = mx + c is (m and c are arbitrary constants)
Choose the correct alternative:
Solution of `("d"x)/("d"y) + "P"x = 0`
Solve x2ydx – (x3 + y3) dy = 0
