## 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){...