Advertisements
Advertisements
Question
Find the differential equation of the family of all non-vertical lines in a plane
Advertisements
Solution
The equation of the family of non-vertical lines in a plane ax + by = 1, b ≠ 0, a ∈ R
Given equation is ax + by = 1 ........(1)
Differentiating equation (1) with respect to ‘x’ we get
`"a" + "b" ("d"y)/("d"x)` = 0
∵ 2 arbitrary constant,
∴ Differentiating twice continuously
Again differentiating above equation with respect to ‘x’, we get
`0 + "b" ("d"^2y)/("d"x^2)` = 0
`("d"^2y)/("d"x^2)` = 0 ......[∵ b ≠ 0]
`("d"^2y)/("d"x^2)` = 0 is a required differential equation.
APPEARS IN
RELATED QUESTIONS
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
c1x3 + c2y2 = 5
Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.
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")`
For the following differential equation find the particular solution satisfying the given condition:
`("x" + 1) "dy"/"dx" - 1 = 2"e"^-"y" , "y" = 0`, when x = 1
Choose the correct option from the given alternatives:
The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is
Choose the correct option from the given alternatives:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of
In the following example verify that the given function is a solution of the differential equation.
`"y" = "e"^"ax" sin "bx"; ("d"^2"y")/"dx"^2 - 2"a" "dy"/"dx" + ("a"^2 + "b"^2)"y" = 0`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = a sin (x + b)
Form the differential equation of all parabolas which have 4b as latus rectum and whose axis is parallel to the Y-axis.
Select and write the correct alternative from the given option for the question
General solution of `y - x ("d"y)/("d"x)` = 0 is
Select and write the correct alternative from the given option for the question
The solution of `("d"y)/("d"x)` = 1 is
Find the differential equation of family of lines making equal intercepts on coordinate axes
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
Form the differential equation of all straight lines touching the circle x2 + y2 = r2
Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis
Find the differential equation of the curve represented by xy = aex + be–x + x2
The general solution of the differential equation of all circles having centre at A(- 1, 2) is ______.
Solve the following differential equation:
`xsin(y/x)dy = [ysin(y/x) - x]dx`
