Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
`"y" - "x" "dy"/"dx" = 0`
Advertisements
उत्तर
`"y" - "x" "dy"/"dx" = 0`
∴ `"x" "dy"/"dx" = "y"`
∴ `1/"x" "dx" = 1/"y" "dy"`
Integrating both sides, we get
`int 1/"x" "dx" = int 1/"y" "dy"`
∴ log |x| = log |y| + log c
∴ log |x| = log |cy|
∴ x = cy
This is the general solution.
APPEARS IN
संबंधित प्रश्न
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = Ae5x + Be-5x
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = c1e2x + c2e5x
Find the differential equation all parabolas having a length of latus rectum 4a and axis is parallel to the axis.
Find the differential equation of the ellipse whose major axis is twice its minor axis.
Find the differential equation of all circles having radius 9 and centre at point (h, k).
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 = 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 = `"e"^"ax"; "x" "dy"/"dx" = "y" log "y"`
Solve the following differential equation:
`"sec"^2 "x" * "tan y" "dx" + "sec"^2 "y" * "tan x" "dy" = 0`
Solve the following differential equation:
`"dy"/"dx" = - "k",` where k is a constant.
Solve the following differential equation:
`(cos^2y)/x dy + (cos^2x)/y dx` = 0
Solve the following differential equation:
`"y"^3 - "dy"/"dx" = "x"^2 "dy"/"dx"`
Solve the following differential equation:
`"dy"/"dx" = "e"^("x + y") + "x"^2 "e"^"y"`
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
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:
`"dy"/"dx" = cos("x + y")`
Reduce the following differential equation to the variable separable form and hence solve:
`("x - y")^2 "dy"/"dx" = "a"^2`
Reduce the following differential equation to the variable separable form and hence solve:
(2x - 2y + 3)dx - (x - y + 1)dy = 0, when x = 0, y = 1.
Choose the correct option from the given alternatives:
x2 + y2 = a2 is a solution of
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:
The solution of `"dy"/"dx" + "y" = cos "x" - sin "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"^2 = "a"("b - x")("b + x")`
In the following example verify that the given function is a solution of the differential equation.
`"x"^2 + "y"^2 = "r"^2; "x" "dy"/"dx" + "r" sqrt(1 + ("dy"/"dx")^2) = "y"`
In the following example verify that the given function is a solution of the differential equation.
`"y" = 3 "cos" (log "x") + 4 sin (log "x"); "x"^2 ("d"^2"y")/"dx"^2 + "x" "dy"/"dx" + "y" = 0`
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"`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = a sin (x + b)
Solve the following differential equation:
`"dy"/"dx" = "x"^2"y" + "y"`
Solve the following differential equation:
x dy = (x + y + 1) dx
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 differential equation of family of lines making equal intercepts on coordinate axes
Form the differential equation of y = (c1 + c2)ex
Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex
The family of curves y = `e^("a" sin x)`, where a is an arbitrary constant, is represented by the differential equation.
Find the differential equation of the family of all non-horizontal lines in a plane
Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis
Find the differential equations of the family of all the ellipses having foci on the y-axis and centre at the origin
The rate of disintegration of a radio active element at time t is proportional to its mass, at the time. Then the time during which the original mass of 1.5 gm. Will disintegrate into its mass of 0.5 gm. is proportional to ______.
The differential equation for all the straight lines which are at the distance of 2 units from the origin is ______.
The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is ______.
Solve the differential equation
cos2(x – 2y) = `1 - 2dy/dx`
Form the differential equation of all concentric circles having centre at the origin.
