Advertisements
Advertisements
Question
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
Options
y = x3 + 2
y = 3x2 + 4
y = 3x3 + 4
y = x3 + 5
Advertisements
Solution
y = x3 + 2
APPEARS IN
RELATED QUESTIONS
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.
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:
`(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:
`("x" + 1) "dy"/"dx" - 1 = 2"e"^-"y" , "y" = 0`, when x = 1
For the following differential equation find the particular solution satisfying the given condition:
`cos("dy"/"dx") = "a", "a" ∈ "R", "y"(0) = 2`
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:
x2 + y2 = a2 is a solution of
In the following example verify that the given function is a solution of the differential equation.
`"xy" = "ae"^"x" + "be"^-"x" + "x"^2; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" + "x"^2 = "xy" + 2`
Solve the following differential equation:
y log y = (log y2 - x) `"dy"/"dx"`
The general solution of `(dy)/(dx)` = e−x is ______.
The family of curves y = `e^("a" sin x)`, where a is an arbitrary constant, is represented by the differential equation.
Form the differential equation of all straight lines touching the circle x2 + y2 = r2
The differential equation of all lines perpendicular to the line 5x + 2y + 7 = 0 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 = ______.
Solve the differential equation
ex tan y dx + (1 + ex) sec2 y dy = 0
The differential equation whose solution represents the family \[x^{2}y=4e^{x}+c\], where c is an arbitrary constant, is
