Advertisements
Advertisements
Question
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Advertisements
Solution
`(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
`(1 + x^2)/x "d"x = (1 + y)y "d"y`
`(1/x + x^2/x) "d"x = (y + y^2) "d"y`
⇒ `[1/x + x] "d"x = (y + y^2) "d"y`
Differentiating on both sides
`int (1/x + x) "d"x = int (y + y^2) "d"y`
⇒ `log x + x^2/2 = y^2/2 + y^3/3 + "c"`
APPEARS IN
RELATED QUESTIONS
Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)
Solve the following differential equation:
`y"d"x + (1 + x^2)tan^-1x "d"y`= 0
Solve the following differential equation:
(ey + 1)cos x dx + ey sin x dy = 0
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Solve the following:
`("d"y)/("d"x) + (3x^2)/(1 + x^3) y = (1 + x^2)/(1 + x^3)`
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.
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is
Choose the correct alternative:
The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is
Form the differential equation having for its general solution y = ax2 + bx
