Advertisements
Advertisements
Question
Find the differential equation of the family of all non-horizontal lines in a plane
Advertisements
Solution
The equation of the family of non horizontal
Lines in a,plane ax + by = 1, a ≠ 0 and b ∈ R
Given equation is ax + by = 1 .......(1)
Differentiating equation (1) with respect to ‘y’, we get
`"a" ("d"x)/("d"y) + "b"` = 0
∵ 2 arbitrary constant,
∴ Differentiating twice continuously
Again differentiating we get
`"a" ("d"^2x)/("d"y^2)` = 0 ......[∵ a ≠ 0]
`("d"^2x)/("d"y^2)` = 0 is a required differential equation.
APPEARS IN
RELATED QUESTIONS
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
x3 + y3 = 4ax
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = Ae5x + Be-5x
In the following example verify that the given expression is a solution of the corresponding differential equation:
xy = log y +c; `"dy"/"dx" = "y"^2/(1 - "xy")`
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = xm; `"x"^2 ("d"^2"y")/"dx"^2 - "mx" "dy"/"dx" + "my" = 0`
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = `"a" + "b"/"x"; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0`
For the following differential equation find the particular solution satisfying the given condition:
`y(1 + log x) dx/dy - x log x = 0, y = e^2,` when x = e
Choose the correct option from the given alternatives:
x2 + y2 = a2 is a solution of
Choose the correct option from the given alternatives:
The solution of `"dy"/"dx" + "y" = cos "x" - sin "x"`
The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is ______.
In the following example verify that the given function is a solution of the differential equation.
`"x"^2 = "2y"^2 log "y", "x"^2 + "y"^2 = "xy" "dx"/"dy"`
Solve the following differential equation:
x dy = (x + y + 1) dx
Solve the following differential equation:
y log y = (log y2 - x) `"dy"/"dx"`
Find the particular solution of the following differential equation:
(x + y)dy + (x - y)dx = 0; when x = 1 = y
Select and write the correct alternative from the given option for the question
Solution of the equation `x ("d"y)/("d"x)` = y log y is
Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax
Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis
Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be –8x, where A and B are arbitrary constants
The elimination of the arbitrary constant m from the equation y = emx gives the differential equation ______.
The differential equation whose solution is (x – h)2 + (y – k)2 = a2 is (where a is a constant) ______.
