Advertisements
Advertisements
प्रश्न
Which of the following differential equations has y = c1 ex + c2 e–x as the general solution?
(A) `(d^2y)/(dx^2) + y = 0`
(B) `(d^2y)/(dx^2) - y = 0`
(C) `(d^2y)/(dx^2) + 1 = 0`
(D) `(d^2y)/(dx^2) - 1 = 0`
Advertisements
उत्तर
This is the required differential equation of the given equation of curve.
Hence, the correct answer is B.
APPEARS IN
संबंधित प्रश्न
Form the differential equation of the family of circles touching the y-axis at the origin.
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3
Form the differential equation of the family of curves represented by y2 = (x − c)3.
Form the differential equation corresponding to y = emx by eliminating m.
Find the differential equation of the family of curves, x = A cos nt + B sin nt, where A and B are arbitrary constants.
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(x − a)2 + 2y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + (y − b)2 = 1
Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x\]
For the differential equation xy \[\frac{dy}{dx}\] = (x + 2) (y + 2). Find the solution curve passing through the point (1, −1).
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} + 3y = e^{mx}\], m is a given real number.
Find one-parameter families of solution curves of the following differential equation:-
\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x}\]
Find one-parameter families of solution curves of the following differential equation:-
\[\left( x \log x \right)\frac{dy}{dx} + y = \log x\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} \cos^2 x = \tan x - y\]
Find one-parameter families of solution curves of the following differential equation:-
\[x \log x\frac{dy}{dx} + y = 2 \log x\]
Write the differential equation representing family of curves y = mx, where m is arbitrary constant.
The differential equation which represents the family of curves y = eCx is
The family of curves in which the sub tangent at any point of a curve is double the abscissae, is given by
Form the differential equation of the family of ellipses having foci on y-axis and centre at the origin.
Form the differential equation representing the family of curves `y2 = m(a2 - x2) by eliminating the arbitrary constants 'm' and 'a'.
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.
The differential equation representing the family of curves y = A sinx + B cosx is ______.
Find the differential equation of system of concentric circles with centre (1, 2).
Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is `(x^2 + y^2)/(2xy)`.
Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abcissa and ordinate of the point.
The differential equation of the family of curves y2 = 4a(x + a) is ______.
Differential equation representing the family of curves y = ex (Acosx + Bsinx) is `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + 2y` = 0
Find the equation of the curve at every point of which the tangent line has a slope of 2x:
From the differential equation of the family of circles touching the y-axis at origin
Form the differential equation of family of circles having centre on y-axis and raduis 3 units
Form the differential equation of the family of hyperbola having foci on x-axis and centre at origin.
