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## Marks 1

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The solution to $$\,\,{x^2}{y^{11}} + x{y^1} - y = 0\,\,$$ is
GATE PI 2015
The solution to $$\,6y{y^1} - 25x = 0\,\,$$ represents a
GATE PI 2015
The homogeneous part of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + qy = r\,\,$$ ( $$... GATE PI 2009 The solutions of the differential equation$${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$are GATE PI 2008 The differential equation$${\left[ {1 + {{\left( {{{d\,y} \over {d\,x}}} \right)}^2}} \right]^3} = {C^2}{\left[ {{{{d^2...
GATE PI 2005
Solve for $$y$$ if $${{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0$$ with $$y(0)=1$$ and $${y^1}\left( 0 \right... GATE PI 1994 ## Marks 2 More Consider the differential equation$$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$with the b... GATE PI 2012 The solution of the differential equation$$\,\,\,{{{d^2}y} \over {d{x^2}}} + 6{{dy} \over {dx}} + 9y = 9x + 6\,\,\,\,$$... GATE PI 2011 Which one of the following differential equations has a solution given by the function$$y = 5\sin \left( {3x + {\pi \o...
GATE PI 2010
The solution of the differential equation $${{dy} \over {dx}} - {y^2} = 1$$ satisfying the condition $$y(0)=1$$ is
GATE PI 2010
The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ with boundary conditions (i) {{dy} \over ...
GATE PI 2009

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