GATE PI
Engineering Mathematics
Differential Equations
Previous Years Questions

## Marks 1

The solution to $$\,6y{y^1} - 25x = 0\,\,$$ represents a
The solution to $$\,\,{x^2}{y^{11}} + x{y^1} - y = 0\,\,$$ is
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 r...
The solutions of the differential equation $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$ are
The differential equation $${\left[ {1 + {{\left( {{{d\,y} \over {d\,x}}} \right)}^2}} \right]^3} = {C^2}{\left[ {{{{d^2}\,y} \over {d\,{x^2}}}} \righ... Solve for$$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) = - 2$$## Marks 2 Consider the differential equation$$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$with the boundary conditions of$$\,\,y\...
The solution of the differential equation $$\,\,\,{{{d^2}y} \over {d{x^2}}} + 6{{dy} \over {dx}} + 9y = 9x + 6\,\,\,\,$$ with $${C_1}$$ and $${C_2}$$...
Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$
The solution of the differential equation $${{dy} \over {dx}} - {y^2} = 1$$ satisfying the condition $$y(0)=1$$ is
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) ...
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