GATE ECE 2008 | Differential Equations Question 22 | Engineering Mathematics

GATE ECE 2008

MCQ (Single Correct Answer)

-0.6

Which of the following is a solution to the differential equation $${d \over {dt}}x\left( t \right) + 3x\left( t \right) = 0,\,\,x\left( 0 \right) = 2?$$

$$x\left( t \right) = 3{e^{ - t}}$$

$$x\left( t \right) = 2\,{e^{ - 3t}}\,$$

$$x\left( t \right) = {{ - 3} \over 2}{t^2}$$

$$x\left( t \right) = 3{t^2}$$

GATE ECE 2007

MCQ (Single Correct Answer)

-0.6

The solution of the differential equation $${k^2}{{{d^2}y} \over {d\,{x^2}}} = y - {y_2}\,\,$$ under the boundary conditions (i) $$y = {y_1}$$ at $$x=0$$ and (ii) $$y = {y_2}$$ at $$x = \propto $$ where $$k$$, $${y_1}$$ and $${y_2}$$ are constant is

$$y = \left( {{y_1} - {y_2}} \right){e^{{{ - x} \over {{k^2}}}}} + {y_2}$$

$$y = \left( {{y_2} - {y_1}} \right){e^{{{ - x} \over k}}} + {y_1}$$

$$y = \left( {{y_1} - {y_2}} \right)\,\sin \,h\left( {{x \over k}} \right) + {y_1}$$

$$y = \left( {{y_1} - {y_2}} \right){e^{{{ - x} \over k}}} + {y_2}$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

For the differential equation $${{{d^2}y} \over {d{x^2}}} + {k^2}y = 0,$$ the boundary conditions are
(i) $$y=0$$ for $$x=0$$ and
(ii) $$y=0$$ for $$x=a$$
The form of non-zero solution of $$y$$ (where $$m$$ varies over all integrals ) are

$$y = \sum\limits_m {{A_m}\sin \left( {{{m\pi x} \over a}} \right)} $$

$$y = \sum\limits_m {{A_m}\cos \left( {{{m\pi x} \over a}} \right)} $$

$$y = \sum\limits_m {{A_m}\,\,{X^{{{m\pi x} \over a}}}} $$

$$y = \sum\limits_m {{A_m}\,\,{e^{{{m\pi x} \over a}}}} $$

GATE ECE 2001

Subjective

-0

Solve the differential equation $${{{d^2}y} \over {d{x^2}}} + y = x\,\,$$ with the following conditions $$(i)$$ at $$x=0, y=1$$ $$(ii)$$ at $$x=0, $$ $${y^1} = 1$$

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