GATE IN
Engineering Mathematics
Differential Equations
Previous Years Questions

## Marks 1

The figure shows the plot of $$y$$ as a function of $$x$$ The function shown in the solution of the differential equation (assuming all initial con...
The type of the partial differential equation $${{\partial f} \over {\partial t}} = {{{\partial ^2}f} \over {\partial {x^2}}}\,\,is$$
With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\... Consider the differential equation$${{dy} \over {dx}} + y = {e^x}$$with$$y(0)=1.$$Then the value of$$y(1)$$is Consider the differential equation$${{dy} \over {dx}} = 1 + {y^2}.$$Which one of the following can be particular solution of this differential equ... The general solution of the differential equation$$\left( {{D^2} - 4D + 4} \right)y = 0$$is of the form (given$$D = {d \over {dx}}$$and$${C_1},...

## Marks 2

The maximum value of the solution $$y$$ $$(t)$$ of the differential equation $$\,\,y\left( t \right) + \mathop y\limits^{ \bullet \,\, \bullet } \left... Consider the differential equation$$\mathop y\limits^{ \bullet \bullet } + 2\,\mathop y\limits^ \bullet + y = 0\,\,$$with boundary conditions ... For initial value problem$$\,\mathop y\limits^{ \bullet \bullet } + 2\,\mathop y\limits^ \bullet + \left( {101} \right)y = \left( {10.4} \right){...
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