Bissoy.com
Doctors Medicines MCQs Q&A

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

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)

Related Questions

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
A 60% spirit solution is mixed with r% spirit solution in the ratio 1 : 3 such that a s% spirit solution is obtained. When a (s/3)% spirit solution is mixed with 55% spirit solution in equal ratio, an (r/2)% spirit solution is obtained. Which of the following can be determined? (A) Value of ‘r’ (B) Value of ‘s’ (C) Volume of the 60% spirit solution mixed initially (D) If 9 liters of r% spirit solution was mixed initially, what was the volume of the s% spirit solution thus obtained?
A wave is first reflected by a boundary P and then by a boundary Q without dissipating energy. If the boundary P is rigid and the boundary Q is non-rigid, then find the fraction of the amplitude of the reflected wave by boundary P to the reflected wave by boundary Q.
A chemical solution appears green when the salt concentration is 8 grams per litre (gpl) and red when it is 10 gpl. Pure water was added to the solution of 1 litre of 15 gpl solution till it turned green. Then 125 ml of the green solution is taken out and x grams of salt is added to the green solution to make it red. Another 500 ml of the final solution was taken out and y litres of green solution is added to get a resultant solution of concentration 9.6 gpl.  Assume adding salt doesn’t change its volume and find the ratio of x and y. 
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
Solution of a differential equation is any function which satisfies the equation.
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
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 ___