GATE PI 2011 | Differential Equations Question 4 | Engineering Mathematics

GATE PI 2011

MCQ (Single Correct Answer)

-0.6

The solution of the differential equation $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 6{{dy} \over {dx}} + 9y = 9x + 6\,\,\,\,$$ with $${C_1}$$ and $${C_2}$$ as constants is

$$y = \left( {{C_1}x + {C_2}} \right){e^{ - 3x}}$$

$$y = {C_1}\,{e^{3x}} + {C_2}\,{e^{ - 3x}}$$

$$y = \left( {{C_1}x + {C_2}} \right){e^{ - 3x}} + x$$

$$y = \left( {{C_1}x + {C_2}} \right){e^{3x}} + x$$

GATE PI 2010

MCQ (Single Correct Answer)

-0.6

Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$

$${{dy} \over {dx}} - {5 \over 3}\cos \left( {3x} \right) = 0$$

$${{dy} \over {dx}} + {5 \over 3}\left( {\cos 3x} \right) = 0$$

$${{{d^2}y} \over {{d^2}\,x}} + 9y = 0$$

$${{{d^2}y} \over {d{x^2}}} - 9y = 0$$

GATE PI 2010

MCQ (Single Correct Answer)

-0.6

The solution of the differential equation $${{dy} \over {dx}} - {y^2} = 1$$ satisfying the condition $$y(0)=1$$ is

$$y = {e^{{x^2}}}$$

$$y = \sqrt x $$

$$\,y = \cot \left( {x + {\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}} \right)$$

$$y = tan\left( {x + {\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}} \right)$$

GATE PI 2009

MCQ (Single Correct Answer)

-0.6

The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ with boundary conditions
(i) $${{dy} \over {dx}} = 1$$ at $$x=0$$
(ii) $${{dy} \over {dx}} = 1$$ at $$x=1$$

$$y=1$$

$$y=x$$

$$y=x+c$$ where $$c$$ is an arbitrary constant.

$$\,y = {C_1}x + {C_2}$$ where $${C_1},\,{C_2}$$ are arbitrary constants