Advertisements
Advertisements
Question
Solve the following:
`("d"y)/("d"x) + (3x^2)/(1 + x^3) y = (1 + x^2)/(1 + x^3)`
Advertisements
Solution
It is of the form `("d"y)/("d"x) + "P"y` = Q
Here P = `(3x^2)/(1 + x^3)`
Q = `(1 + x^2)/(1 + x^3)`
`int "Pd"x = int (3x^2)/(1 + x^3) "d"x`
= `log (1 + x^3)`
I.F = `"e"^(int Pdx)`
= `"e"^(log (1 + x^3))`
= `(1 + x^3)`
The required solution is
y(I.F) = `int "Q" ("I.F") "d"x + "c"`
`y(1 + x^3) = int ((1 + x^2))/((1 + x^3)) xx (1 + x^3) "d"x + "c"`
`y(1 + x^3) = int(1 + x^2) "d"x + "c"`
⇒ `y(1 + x^3) = x + x^3/3 + "c"`
APPEARS IN
RELATED QUESTIONS
Solve the following differential equation:
(ey + 1)cos x dx + ey sin x dy = 0
Solve the following differential equation:
`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - 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
Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0
Solve: `log(("d"y)/("d"x))` = ax + by
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) = x + y`
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
Solve the following:
`("d"y)/(""dx) + y cos x = sin x cos x`
Solve `x ("d"y)/(d"x) + 2y = x^4`
Solve x2ydx – (x3 + y3) dy = 0
