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A function n(x) satisfies the differential equation $$\frac{{{{\text{d}}^2}{\text{n}}\left( {\text{x}} \right)}}{{{\text{d}}{{\text{x}}^2}}} - \frac{{{\text{n}}\left( {\text{x}} \right)}}{{{{\text{L}}^2}}} = 0$$    where L is a constant. The boundary conditions are: n(0) = K and n($$\infty $$) = 0. The solution to this equation is

Correct Answer: n(x) = K exp(-x/L)

The figure shows the plot of y as a function of x
Differential Equations mcq question image
The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is

Solution of a differential equation is any function which satisfies the equation.

The solution to the differential equation $$\frac{{{{\text{d}}^2} \cdot {\text{u}}}}{{{\text{d}}{{\text{x}}^2}}} - {\text{k}}\frac{{{\text{du}}}}{{{\text{dx}}}} = 0$$    is where k is constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

The solution of differential equation $$\frac{{{{\text{d}}^2}{\text{u}}}}{{{\text{d}}{{\text{x}}^2}}} - {\text{K}}\frac{{{\text{du}}}}{{{\text{dx}}}} = 0$$    where K is constant, subjected to boundary conditions u(0) = 0 and u(L) = U is

Singular solution of a differential equation is one that cannot be obtained from the general solution gotten by the usual method of solving the differential equation.

A differential equation is given as
$${{\text{x}}^2}\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} - 2{\text{x}}\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{y}} = 4$$
The solution of differential equation in terms of arbitrary constant C1 and C2 is

The function f(t) satisfies the differential equation $$\frac{{{{\text{d}}^2}{\text{f}}}}{{{\text{d}}{{\text{t}}^2}}} + {\text{f}} = 0$$   and the auxiliary conditions, f(0) = 0, $$\frac{{{\text{df}}}}{{{\text{dt}}}}\left( 0 \right) = 4.$$  The Laplace transform of f(t) is given by

In Finite Element Methods (FEM), a boundary value problem is a set of differential equations with a solution, which also satisfies some additional constraints, known as ___

The nature of normal grain growth in the presence of a second phase deserves special consideration. The moving boundaries will be attached to the particles exert a pulling force on the boundary restricting its motion. Therefore if the boundary intersects the particle surface at 90° the particle will feel a pull of (2πrγcosΘ)*sinΘ. This will be counterbalanced by an equal and opposite force acting on the boundary. As the boundary moves over the particle surface Θ changes and the drag reaches a maximum value, this happens when Θ becomes______

The boundary layer thickness at a distance of l m from the leading edge of a flat plate, kept at zero angle of incidence to the flow direction, is O.l cm. The velocity outside the boundary layer is 25 ml sec. The boundary layer thickness at a distance of 4 m is (Assume that boundary layer is entirely laminar)