GATE ECE 2018 | Differential Equations Question 4 | Engineering Mathematics

GATE ECE 2018

MCQ (Single Correct Answer)

-0.67

A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation

$${{dy} \over {dx}} = {{{x^2} + {y^2}} \over {2y}} + {y \over x}$$. The equation that describes the curve is

$$\ln \left( {1 + {{{y^2}} \over {{x^2}}}} \right) = x - 1$$

$${1 \over 2}\ln \left( {1 + {{{y^2}} \over {{x^2}}}} \right) = x - 1$$

$${1 \over 2}\ln \left( {1 + {y \over x}} \right) = x - 1$$

$$\ln \left( {1 + {y \over x}} \right) = x - 1$$

GATE ECE 2017 Set 1

MCQ (Single Correct Answer)

-0.6

Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left( {x + y - 1} \right)^2}$$ , where $$x,$$ $$y$$ are real ?

$$y = 1 + x + {\tan ^{ - 1}}\left( {x + c} \right),$$ where $$c$$ is a constant

$$y = 1 + x + \tan \left( {x + c} \right),$$ where $$c$$ is a constant

$$y = 1 - x + {\tan ^{ - 1}}\left( {x + c} \right),$$ where $$c$$ is a constant

$$y = 1 - x + \tan \left( {x + c} \right),$$ where $$c$$ is a constant

GATE ECE 2016 Set 3

MCQ (Single Correct Answer)

-0.6

The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}} + 36y = 0\,\,$$ with $$\,y\left( 0 \right) = 3\,\,$$ and $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 0}} = - 36\,\,$$

$$\left( {3 - 18x} \right){e^{ - 6x}}$$

$$\left( {3 + 25x} \right){e^{ - 6x}}$$

$$\left( {3 + 20x} \right){e^{ - 6x}}$$

$$\left( {3 - 12x} \right){e^{ - 6x}}$$

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

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

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

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

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

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