Advertisements
Advertisements
प्रश्न
Find the differential equation of the curve represented by xy = aex + be–x + x2
Advertisements
उत्तर
Given xy = aex + be–x + x2 ........(1)
Where a and b are aribitrary constant,
Differentiate equation (1) twice successively,
Because we have two arbitray constant.
`x ("d"y)/("d"x) + y(1)` = aex – be–x + 2x .......(2)
`x ("d"^2y)/("d"x^2) + ("d")/("d"x) (1) + ("d"y)/("d"x)` = aex + be–x + 2
`x ("d"^2y)/("d"x^2) + (2"d"y)/("d"x)` = aex + be–x + 2 ......(3)
From (1), we get xy – x2 = aex + be–x ........(4)
Substituting equation (4) in (3), we get
∴ `x ("d"^2y)/("d"x^2) + (2"d"y)/("d"x) - xy + x^2 - 2` = 0 is the required differential equation.
APPEARS IN
संबंधित प्रश्न
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y2 = (x + c)3
Find the differential equation of the ellipse whose major axis is twice its minor axis.
Solve the following differential equation:
`(cos^2y)/x dy + (cos^2x)/y dx` = 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
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:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = `"Ae"^(3"x" + 1) + "Be"^(- 3"x" + 1)`
Solve the following differential equation:
x dy = (x + y + 1) dx
Find the particular solution of the following differential equation:
y(1 + log x) = (log xx) `"dy"/"dx"`, when y(e) = e2
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 all ellipse whose major axis is twice the minor axis
Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex
The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of X-axis is ______.
If y = (tan–1 x)2 then `(x^2 + 1)^2 (d^2y)/(dx^2) + 2x(x^2 + 1) (dy)/(dx)` = ______.
The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is ______.
Form the differential equation of all concentric circles having centre at the origin.
The differential equation whose solution represents the family \[x^{2}y=4e^{x}+c\], where c is an arbitrary constant, is
