Engineering Mathematics
Differential Equations
Practice questions from Differential Equations.
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IncorrectThe function satisfies
where and denote the first and second derivatives of respectively.
Given and , the maximum value of over is _________ (rounded off to two decimal places).
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Sign in to UnlockThe general form of the complementary function of a differential equation is given by where A and B are real constants determined by the initial condition. The corresponding differential equation is__________.
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Sign in to UnlockConsider the following partial differential equation (PDE)
where and are distinct positive real numbers. Select the combination(s) of values of the real parameters and such that is a solution of the given PDE.
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Sign in to UnlockConsider the following wave equation,
Which of the given options is/are solution(s) to the given wave equation?
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Sign in to UnlockConsider the differential equation given below:
The integrating factor of the differential equation is
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Sign in to UnlockThe general solution of is
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Sign in to UnlockWhich one of the following options contains two solutions of the differential equation ?
and
and
and
and
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Sign in to UnlockThe families of curves represented by the solution of the equation
For n=-1 and n=+1, respectively, are
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Sign in to UnlockConsider the homogeneous ordinary differential equation
with as a general solution. Given that
The value of , rounded off to two decimal places, is ____________.
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Sign in to UnlockA curve passes through the pointand satisfies the differential equation. The equation that describes the curve is
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Sign in to UnlockWhich one of the following is the general solution of the first order differential equation
where x, y are real?
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Sign in to UnlockThe general solution of the differential equation. In terms of arbitrary constants is
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Sign in to UnlockThe particular solution of the initial value problem given below is
with y(0)=3 and
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Sign in to UnlockThe solution of the differential equation with y(0)=y'(0)=1 is
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Sign in to UnlockThe general solution of the differential equation is
( c is a constant)
( c is a constant)
( c is a constant)
( c is a constant)
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Sign in to UnlockConsider the differential equation with initial condition x(0) = 1. The response x(t) for t > 0 is
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Sign in to UnlockConsider the differential equation. Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
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Sign in to UnlockIf the characteristic equation of the differential equation ,has two equal roots, then the values of α are
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Sign in to UnlockWhich ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?
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Sign in to UnlockIf a and b are constants, the most general solution of the differential equation is
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Sign in to UnlockWith initial values y(0) = y' (0) = 1, the solution of the differential equation at x=1 is _____.
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Sign in to UnlockWith initial condition x(1) =0.5, the solution of the differential equation, is
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Sign in to UnlockConsider the differential equation
With and
The numerical value of is
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Sign in to UnlockThe solution of the differential equation, is
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Sign in to UnlockA function n(x) satisfied the differential equation where L is a constant. The boundary conditions are: and . The solution to this equation is
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Sign in to UnlockThe order of the differential equation is
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Sign in to UnlockMatch each differential equation in Group I to its family of solution curves from Group II
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Sign in to UnlockWhich of the following is a solution to the differential equation ?
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Sign in to UnlockThe solution of the differential equation under the boundary conditions
(i) , at x = 0 and
(ii) at x = ∞, where k, and are constants, is
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Sign in to UnlockA solution for the differential equation With initial condition is:
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Sign in to UnlockFor the differential equation the boundary conditions are
(i) y = 0 for x = 0 and
(ii) y = 0 for x = a
The form of non-zero solutions of y (where m varies over all integers) are
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Sign in to UnlockThe following differential equation has
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Sign in to UnlockA solution of the following differential equation is given by
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Sign in to UnlockFind the correct statement for the given differential equations
(A)
(B)
(C)
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Sign in to UnlockThe differential equation, , is:
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