GATE PI 2015 | Differential Equations Question 2 | Engineering Mathematics

The homogeneous part of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + qy = r\,\,$$ ( $$p, q, r$$ are constants) has real distinct roots if

$${p^2} - 4q > 0$$

$${p^2} - 4q < 0$$

$${p^2} - 4q = 0$$

$${p^2} - 4q = r$$

GATE PI 2008

MCQ (Single Correct Answer)

-0.3

The solutions of the differential equation $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$ are

$${e^{ - \left( {1 + i} \right)x}},{e^{ - \left( {1 - i} \right)x}}$$

$${e^{\left( {1 + i} \right)x}},\,\,{e^{\left( {1 - i} \right)x}}$$

$${e^{ - \left( {1 + i} \right)x}},\,\,{e^{\left( {1 + i} \right)x}}$$

$${e^{\left( {1 + i} \right)x}},\,\,{e^{ - \left( {1 + i} \right)x}}$$

GATE PI 2005

MCQ (Single Correct Answer)

-0.3

The differential equation $${\left[ {1 + {{\left( {{{d\,y} \over {d\,x}}} \right)}^2}} \right]^3} = {C^2}{\left[ {{{{d^2}\,y} \over {d\,{x^2}}}} \right]^2}$$ is of

$${2^{nd}}$$ order and $${3^{rd}}$$ degree

$${3^{rd}}$$ order and $${2^{nd}}$$ degree

$${2^{nd}}$$ order and $${2^{nd}}$$ degree

$${3^{rd}}$$ order and $${3^{rd}}$$ degree

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Questions Asked from Marks 1

GATE PI 2015 (2) GATE PI 2009 (1) GATE PI 2008 (1) GATE PI 2005 (1) GATE PI 1994 (1)

GATE PI Subjects

Fluid Mechanics

Metrology

Theory of Machines

Engineering Mathematics

Heat Transfer

Machine Tools and Machining

Industrial Engineering

Engineering Mechanics

Strength of Materials

Thermodynamics

Machine Design

Casting

Joining of Materials

Metal Forming