AIEEE 2011 | Differential Equations Question 212 | Mathematics

Let $$I$$ be the purchase value of an equipment and $$V(t)$$ be the value after it has been used for $$t$$ years. The value $$V(t)$$ depreciates at a rate given by differential equation $${{dv\left( t \right)} \over {dt}} = - k\left( {T - t} \right),$$ where $$k>0$$ is a constant and $$T$$ is the total life in years of the equipment. Then the scrap value $$V(T)$$ of the equipment is

$$I - {{k{T^2}} \over 2}$$

$$I - {{k{{\left( {T - t} \right)}^2}} \over 2}$$

$${e^{ - kT}}$$

$${T^2} - {1 \over k}$$

AIEEE 2010

MCQ (Single Correct Answer)

-1

Solution of the differential equation

$$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x <{\pi \over 2}$$ is :

$$y\sec x = \tan x + c$$

$$y\tan x = \sec x + c$$

$$\tan x = \left( {\sec x + c} \right)y$$

$$\sec x = \left( {\tan x + c} \right)y$$

AIEEE 2009

MCQ (Single Correct Answer)

-1

Out of Syllabus

The differential equation which represents the family of curves $$y = {c_1}{e^{{c_2}x}},$$ where $${c_1}$$ , and $${c_2}$$ are arbitrary constants, is

$$y'' = y'y$$

$$yy'' = y'$$

$$yy'' = {\left( {y'} \right)^2}$$

$$y' = {y^2}$$

AIEEE 2008

MCQ (Single Correct Answer)

-1

The solution of the differential equation

$${{dy} \over {dx}} = {{x + y} \over x}$$ satisfying the condition $$y(1)=1$$ is :

$$y = \ln x + x$$

$$y = x\ln x + {x^2}$$

$$y = x{e^{\left( {x - 1} \right)}}\,$$

$$y = x\,\ln x + x$$