Advertisements
Advertisements
Question
Choose the correct option from the given alternatives:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of
Options
`("d"^2"y")/"dx"^2 + "yx" + ("dy"/"dx")^2 = 0`
`"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
`"y" ("d"^2"y")/"dx"^2 + 2 ("dy"/"dx")^2 + "y" = 0`
`"xy" "dy"/"dx" + "y" ("d"^2"y")/"dx"^2 = 0`
Solution
`"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
Hint:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` .....(1)
∴ `1/"a"^2 xx "2x" - 1/"b"^2 xx "2y" "dy"/"dx" = 0`
∴ `"x"/"a"^2 - "y"/"b"^2 "dy"/"dx" = 0` ....(2)
and `1/"a"^2 xx 1 - 1/"b"^2 ["y" ("d"^2"y")/"dx"^2 + ("dy"/"dx")^2] = 0` ....(3)
Equations (1), (2) and (3) are consistent
∴ `|("x"^2, - "y"^2, 1),("x", -"y" "dy"/"dx", 0),(1, -["y" ("d"^2"y")/"dx"^2 + ("dy"/"dx")^2], 0)| = 0`
∴ `"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
APPEARS IN
RELATED QUESTIONS
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
c1x3 + c2y2 = 5
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = e−2x (A cos x + B sin x)
Form the differential equation of all parabolas whose axis is the X-axis.
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = e-x + Ax + B; `"e"^"x" ("d"^2"y")/"dx"^2 = 1`
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`
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = `"e"^"ax"; "x" "dy"/"dx" = "y" log "y"`
Solve the following differential equation:
`log ("dy"/"dx") = 2"x" + 3"y"`
Solve the following differential equation:
`"sec"^2 "x" * "tan y" "dx" + "sec"^2 "y" * "tan x" "dy" = 0`
Solve the following differential equation:
`2"e"^("x + 2y") "dx" - 3"dy" = 0`
For the following differential equation find the particular solution satisfying the given condition:
`(e^y + 1) cos x + e^y sin x. dy/dx = 0, "when" x = pi/6,` y = 0
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
Reduce the following differential equation to the variable separable form and hence solve:
`("x - y")^2 "dy"/"dx" = "a"^2`
Choose the correct option from the given alternatives:
The differential equation of y = `"c"^2 + "c"/"x"` is
Choose the correct option from the given alternatives:
The solution of `"dy"/"dx" + "y" = cos "x" - sin "x"`
Choose the correct option from the given alternatives:
The solution of the differential equation `"dy"/"dx" = sec "x" - "y" tan "x"`
The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is ______.
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = `"Ae"^(3"x" + 1) + "Be"^(- 3"x" + 1)`
Form the differential equation of all parabolas which have 4b as latus rectum and whose axis is parallel to the Y-axis.
Solve the following differential equation:
`"dy"/"dx" = ("2y" - "x")/("2y + x")`
Solve the following differential equation:
`"dy"/"dx" + "y cot x" = "x"^2 "cot x" + "2x"`
Solve the following differential equation:
`"dx"/"dy" + "8x" = 5"e"^(- 3"y")`
Find the particular solution of the following differential equation:
(x + y)dy + (x - y)dx = 0; when x = 1 = y
Find the particular solution of the following differential equation:
`2e ^(x/y) dx + (y - 2xe^(x/y)) dy = 0," When" y (0) = 1`
Select and write the correct alternative from the given option for the question
The solutiion of `("d"y)/("d"x) + x^2/y^2` = 0 is
Form the differential equation of family of standard circle
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
Find the differential equation from the relation x2 + 4y2 = 4b2
The differential equation having y = (cos-1 x)2 + P (sin-1 x) + Q as its general solution, where P and Q are arbitrary constants, is
Find the differential equations of the family of all the ellipses having foci on the y-axis and centre at the origin
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 ______.
For the curve C: (x2 + y2 – 3) + (x2 – y2 – 1)5 = 0, the value of 3y' – y3 y", at the point (α, α), α < 0, on C, is equal to ______.
The differential equation of all parabolas whose axis is Y-axis, is ______.
The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is ______.
Find the particular solution of the differential equation `x^2 dy/dx + y^2 = xy dy/dx`, if y = 1 when x = 1.
