What is the order of the differential equation given by dy / dx + 4y = sinx?
If y = x is a solution of x2y" + x y' - y = 0,then the second linearly independent solution of the above equation is.
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Consider the differential equation y” + 9y = 0 with the boundary conditions, y(0) = 0, y(2π) = 1, then the differential equation has
The integrating factor of the differential equation,
(xy2 sin xy + y cosxy )dx + (x2y sin x y - x cos xy )dy - 0 is
The difference between the greatest and the least values of the function,
Let
then number of points (where f(x) attains its minimum value )is ,
In [0,1] .Lagrange’s mean value theorem is NOT .applicable to
The orthogonal trajectories for the family of circles touching the y-axis at the origin is ,
The global maxima of f(x) = [2{-x2 + x + 1}] is , where {x} denotes fractional part of x and [-] denotes greatest integer function
Consider the differential equation where a,b > 0 and y(0)=y0 when x → ∞ then solution y(x) tends to
A function f is such that and f has local maximum of -20 at x = a , then f(x) may be ,
Consider the differential equation where
and y(0) = 0, if y(x) be the continuous solution on [ 0, ∞) then
The initial value problem has a unique solution if ( x0,y0 ) equals,
The polynomial function f(x) of degree 6 ,which satisfies,
and has local maxima at x =1 and local minimum at x = 0 and x =2, is
The set of all the values of K for which the point of minimum of the function f(x) = 1 + K2x - x3, satisfy the inequality
If are three solutions of a non - homogeneous linear differential equation where P(x), Q(x) and R(x) are continuous function on [a, b] with a > 0, then its particular solution w.r. to the conditions y(0) = 0 y.O) = 1
Let y(x) be the solution of the different equation such that y(0) = 2 and y'(0) = 2α. Then the values of such that the in infimum of the set is greater than or equal to1 , are
The differential equation satisfied by the system of parabolas y2 = 4a(x+ a) is
if is defined by
Consider the differential equation , where a,b > 0 and y(0) = y0 when
, then solution y(x) tends to
Let y(x) be the solution of the differential equation,
satisfying the condition y(0) = 2. then which of the following is not true ?
consider the following's two inqualities as:
then which one is true?
Consider the follwing two statements
(I) for all x in [0,1] , let the second derivative f"(x) of a function f(x) exist and satisfy if f(0) = f(1) then
then which one is true?
Let y(x) be a continous solution of the intial value problem
then which of the follwoing is true ?
A differentiable function f(x) has relative minimum at x = 0, then the function y = f(x) +ax+ b, has a relative minimum at x = 0 for
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