GATE CE 2004 | Differential Equations Question 39 | Engineering Mathematics

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

$$x = a\,{e^{ - kt}}$$

$$\,{1 \over x} = {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle a$}} + k\,t$$

$$x = a\left( {1 - {e^{ - kt}}} \right)$$

$$x = a\, + k\,t$$

GATE CE 2001

MCQ (Single Correct Answer)

-0.6

The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \right) = - 3$$ is where $${{{d^2}y} \over {d{x^2}}} = 3x - 2$$

$$y = {{{x^3}} \over 3} - {{{x^2}} \over 2} = 3x - 2$$

$$y = 3{x^3} - {{{x^2}} \over 2} - 5x + 2$$

$$y = {{{x^3}} \over 2} - {x^2} - 5{x \over 2} + 2$$

$$y = {x^3} - {{{x^2}} \over 2} + 5x + {3 \over 2}$$

GATE CE 1998

Subjective

-0

Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$

GATE CE 1997

MCQ (Single Correct Answer)

-0.6

The differential equation $${{dy} \over {dx}} + py = Q,$$ is a linear equation of first order only if,

$$P$$ is a constant but $$Q$$ is a function of $$y$$

$$P$$ and $$Q$$ are functions of $$y$$ (or) constants

$$P$$ is a function of $$y$$ but $$Q$$ is a constant

$$P$$ and $$Q$$ are functions of $$x$$ (or) constants

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GATE CE Subjects

Engineering Mechanics

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Hydrology

Irrigation

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude