Advertisements
Advertisements
Question
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
Options
y = aex
y = be2x
y = be−2x
y = eax
Advertisements
Solution
y = eax
APPEARS IN
RELATED QUESTIONS
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y2 = (x + c)3
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 - a)2 = 4(x - b)
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.
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:
`log ("dy"/"dx") = 2"x" + 3"y"`
Solve the following differential equation:
`"y" - "x" "dy"/"dx" = 0`
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"`
For the following differential equation find the particular solution satisfying the given condition:
`cos("dy"/"dx") = "a", "a" ∈ "R", "y"(0) = 2`
Solve the following differential equation:
(x2 + y2)dx - 2xy dy = 0
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:
x2 + y2 = a2 is a solution of
Choose the correct option from the given alternatives:
The solution of `"dy"/"dx" = ("y" + sqrt("x"^2 - "y"^2))/"x"` is
Choose the correct option from the given alternatives:
The solution of `"dy"/"dx" + "y" = cos "x" - sin "x"`
The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` 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 + "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" = "e"^"ax" sin "bx"; ("d"^2"y")/"dx"^2 - 2"a" "dy"/"dx" + ("a"^2 + "b"^2)"y" = 0`
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)
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
(y - a)2 = b(x + 4)
Solve the following differential equation:
`"dy"/"dx" = ("2y" - "x")/("2y + x")`
Solve the following differential equation:
x dy = (x + y + 1) dx
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
Find the differential equation of family of all ellipse whose major axis is twice the minor axis
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 circles passing through the origin and having their centres on the x-axis
Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis
The general solution of the differential equation of all circles having centre at A(- 1, 2) 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 whose solution is (x – h)2 + (y – k)2 = a2 is (where a is a constant) ______.
The differential equation of all circles passing through the origin and having their centres on the X-axis is ______.
Form the differential equation whose general solution is y = a cos 2x + b sin 2x.
A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.
