Advertisements
Advertisements
प्रश्न
Find the curve whose gradient at any point P(x, y) on it is `(x - "a")/(y - "b")` and which passes through the origin
उत्तर
The gradient of the curve at P(x, y)
`("d"y)/("d"x) = (x - "a")/(y - "b")`
(y – b) dy = (x – a) dx
Integrating on both sides
`int (y - "b") "d"y = int (x - "a") "d"x`
⇒ `(y -- "b")^2/2 = (x - )^2/2 + "c"`
Multiply each term by 2
∴ (y – b)2 = (x – a)2 + 2c .........(1)
Since the curve passes through the origin (0, 0)
Equation (1)
(0 – b)2 = (0 – a)2 + 2c
b2 = a2 + 2c
b2 – a2 = 2c .......(2)
Substitute equation (2) and (1)
(y – b)2 = (x – a)2 + b2 – a2
APPEARS IN
संबंधित प्रश्न
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 the following differential equation:
`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`
Choose the correct alternative:
The solution of `("d"y)/("d"x) = 2^(y - x)` is
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Choose the correct alternative:
The number of arbitrary constants in the general solutions of order n and n +1are respectively
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
Solve `x ("d"y)/(d"x) + 2y = x^4`
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
