GATE ECE 2015 Set 1 | Differential Equations Question 12 | Engineering Mathematics

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.6

The Solution of the differential equation $$\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ with $$\,y\left( 0 \right) = {y^1}\left( 0 \right) = 1\,\,$$ is

$$\left( {2 - t} \right){e^t}$$

$$\left( {1 + 2t} \right){e^{ - t}}$$

$$\left( {2 + t} \right){e^{ - t}}$$

$$\left( {1 - 2t} \right){e^t}$$

GATE ECE 2014 Set 4

Numerical

-0

With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 4y = 0\,\,$$ at $$x=1$$ is ________.

Your input ____

GATE ECE 2014 Set 3

MCQ (Single Correct Answer)

-0.6

Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independent and dependent variables respectively?

$${{dy} \over {dx}} + xy = {e^{ - x}}$$

$${{dy} \over {dx}} + xy = 0$$

$${{dy} \over {dx}} + xy = {e^{ - y}}$$

$${{dy} \over {dx}} + {e^{ - y}} = 0$$

GATE ECE 2010

MCQ (Single Correct Answer)

-0.6

A function $$n(x)$$ satisfies the differential equation $${{{d^2}n\left( x \right)} \over {d{x^2}}} - {{n\left( x \right)} \over {{L^2}}} = 0$$ where $$L$$ is a constant. The boundary conditions are $$n(0)=k$$ and $$n\left( \propto \right) = 0.$$ The solution to this equation is

$$n\left( x \right) = k\,\exp \left( {{{ - x} \over L}} \right)$$

$$n\left( x \right) = k\,\exp \left( {{{ - x} \over {\sqrt L }}} \right)$$

$$n\left( x \right) = {k^2}\,\exp \left( {{{ - x} \over L}} \right)$$

$$n\left( x \right) = {k^2}\,\exp \left( {{{ - x} \over {\sqrt L }}} \right)$$

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