Advertisements
Advertisements
Question
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Advertisements
Solution
`y(1 - x) - x ("d"y)/("d"x)` = 0
`y(1 - x) = x ("d"y)/("d"x)`
⇒ `((1 - x))/x "d"x = 1/y "d"y`
`(1/x - x/x) "d"x = 1/y "d"y`
⇒ `(1/x - 1) "d"x = 1/y "d"y`
Integrating on both sides
`int (1/x - 1) "d"x = int 1/y "d"y`
`log x - x = log y + "c"`
APPEARS IN
RELATED QUESTIONS
Solve the following differential equation:
`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0
Solve the following differential equation:
`y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y`
Choose the correct alternative:
The solution of `("d"y)/("d"x) = 2^(y - x)` is
Solve: `("d"y)/("d"x) = "ae"^y`
Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Solve the following homogeneous differential equation:
(y2 – 2xy) dx = (x2 – 2xy) dy
Solve the following homogeneous differential equation:
The slope of the tangent to a curve at any point (x, y) on it is given by (y3 – 2yx2) dx + (2xy2 – x3) dy = 0 and the curve passes through (1, 2). Find the equation of the curve
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is
Form the differential equation having for its general solution y = ax2 + bx
