Differential Equations MCQs Question and Answer in Engineering Maths

The general solution of the differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + 2\frac{{{\text{dy}}}}{{{\text{dx}}}} - 5{\text{y}} = 0$$     in terms of arbitrary constants K₁ and K₂ is

General solution of the Cauchy-Euler equation $${{\text{x}}^2}\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} - 7{\text{x}}\frac{{{\text{dy}}}}{{{\text{dx}}}} + 16{\text{y}} = 0$$     is

Biotransformation of an organic compound having concentration (x) can be modeled using an ordinary differential equation $$\frac{{{\text{dx}}}}{{{\text{dt}}}} + {\text{k}}{{\text{x}}^2} = 0,$$   where k is the reaction rate constant. If x = a at t = 0, the solution of the equation is

The solution of initial value problem; $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = 2\frac{{\partial {\text{u}}}}{{\partial {\text{t}}}} + {\text{u,}}$$   where u(x, 0) = 6e^-3x 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

The solutions of differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + \frac{{{\text{2dy}}}}{{{\text{dx}}}} + 2{\text{y}} = 0$$     are

It is given that y'' + 2y' + y = 0, y(0) = 0, y(1) = 0. What is y (0.5)?

A function y(t), such that y(0) = 1 and y(1) = 3e^-1, is a solution of the differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{t}}^2}}} + 2\frac{{{\text{dy}}}}{{{\text{dt}}}} + {\text{y}} = 0.$$    Then y(2) is

A curve passes through the point (x = 1, y = 0) and satisfies the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \frac{{{{\text{x}}^2} + {{\text{y}}^2}}}{{2{\text{y}}}} + \frac{{\text{y}}}{{\text{x}}}.$$    The equation that describes the curve is

The differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 4{\text{y}} = 5$$   is valid in the domain 0 ≤ x ≤ 1 with y(0) = 2.25. The solution of differential equation is