Advertisements
Advertisements
प्रश्न
Select and write the correct alternative from the given option for the question
The solution of `("d"y)/("d"x)` = 1 is
विकल्प
x + y = c
xy = c
x2 + y2 = c
y – x = c
Advertisements
उत्तर
y – x = c
संबंधित प्रश्न
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = A cos (log x) + B sin (log x)
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
(y - a)2 = 4(x - b)
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = a + `"a"/"x"`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = e−2x (A cos x + B sin x)
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 family of lines parallel to the line 2x + 3y + 4 = 0.
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 = `(sin^-1 "x")^2 + "c"; (1 - "x"^2) ("d"^2"y")/"dx"^2 - "x" "dy"/"dx" = 2`
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`
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:
`("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
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"`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = a sin (x + b)
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.
Form the differential equation of all the lines which are normal to the line 3x + 2y + 7 = 0.
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
The general solution of `(dy)/(dx)` = e−x is ______.
Find the general solution of `("d"y)/("d"x) = (1 + y^2)/(1 + x^2)`
Form the differential equation of family of standard circle
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 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 equation of the family of all non-horizontal lines in a plane
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 family of parabolas with vertex at (0, –1) and having axis along the y-axis
Choose the correct alternative:
The slope at any point of a curve y = f(x) is given by `("d"y)/("d"x) - 3x^2` and it passes through (-1, 1). Then the equation of the curve is
If m and n are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and X-axis as its axis, then mn - m + n = ______.
The differential equation for all the straight lines which are at the distance of 2 units from the origin is ______.
Form the differential equation of all lines which makes intercept 3 on x-axis.
The differential equation whose solution is (x – h)2 + (y – k)2 = a2 is (where a is a constant) ______.
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 ______.
If y = (tan–1 x)2 then `(x^2 + 1)^2 (d^2y)/(dx^2) + 2x(x^2 + 1) (dy)/(dx)` = ______.
The differential equation for a2y = log x + b, is ______.
Find the particular solution of the differential equation `x^2 dy/dx + y^2 = xy dy/dx`, if y = 1 when x = 1.
