GATE IN 2010 | Differential Equations Question 6 | Engineering Mathematics

GATE IN 2010

MCQ (Single Correct Answer)

-0.3

Consider the differential equation $${{dy} \over {dx}} + y = {e^x}$$ with $$y(0)=1.$$ Then the value of $$y(1)$$ is

$$e + {e^{ - 1}}$$

$${1 \over 2}\left[ {e - {e^{ - 1}}} \right]$$

$${1 \over 2}\left[ {e + {e^{ - 1}}} \right]$$

$$2\left[ {e - {e^{ - 1}}} \right]$$

GATE IN 2008

MCQ (Single Correct Answer)

-0.3

Consider the differential equation $${{dy} \over {dx}} = 1 + {y^2}.$$ Which one of the following can be particular solution of this differential equation ?

$$y = tan(x+3)$$

$$y=(tanx)+3$$

$$x=tan(y+3)$$

$$x=(tany)+3$$

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

The general solution of the differential equation $$\left( {{D^2} - 4D + 4} \right)y = 0$$ is of the form (given $$D = {d \over {dx}}$$ and $${C_1},{C_2}$$ are constants)

$${C_1}\,{e^{2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,{e^{ - 2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,{e^{2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,x\,{e^{2x}}$$

GATE IN Subjects

Engineering Mathematics

Linear Algebra Calculus Vector Calculus Probability and Statistics Differential Equations Numerical Methods Complex Variable Transform Theory