Advertisements
Advertisements
प्रश्न
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Advertisements
उत्तर
`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
संबंधित प्रश्न
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:
`(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:
If sin x is the integrating factor of the linear differential equation `("d"y)/("d"x) + "P"y = "Q"`, then P is
Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0
Find the curve whose gradient at any point P(x, y) on it is `(x - "a")/(y - "b")` and which passes through the origin
Solve the following homogeneous differential equation:
An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x2 + y2) dy = xy dx where x represents the number of units (in thousands). What is the total revenue function?
Solve the following:
`("d"y)/("d"x) - y/x = x`
Solve the following:
`("d"y)/(""dx) + y cos x = sin x cos x`
Choose the correct alternative:
Solution of `("d"x)/("d"y) + "P"x = 0`
Choose the correct alternative:
The differential equation of x2 + y2 = a2
