GATE PI 2012 | Differential Equations Question 3 | Engineering Mathematics

GATE PI 2012

MCQ (Single Correct Answer)

-0.6

Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ and $$\,\,y\left( 1 \right) = 1.\,\,\,$$ The complete solution of the differential equation is

$${x^2}$$

$$\sin \left( {{{\pi x} \over 2}} \right)$$

$${e^x}\sin \left( {{{\pi x} \over 2}} \right)$$

$${e^{ - x}}\sin \left( {{{\pi x} \over 2}} \right)$$

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 $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$

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

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

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

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