Using given data points tabulated below, a straight line passing through the origin is fitted using least squares method. The slope of the line is

If $${x^2}\left( {{{d\,y} \over {d\,x}}} \right) + 2xy = {{2\ln x} \over x}$$ and $$y(1)=0$$ then what is $$y(e)$$?

The complete solution of the ordinary differential equation $${{{d^2}y} \over {d\,{x^2}}} + p{{dy} \over {dx}} + qy = 0$$ is $$\,y = {c_1}\,{e^{ - x}} + {C_2}\,{e^{ - 3x}}\,\,$$ then $$p$$ and $$q$$ are

Which of the following is a solution of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + \left( {q + 1} \right)y = 0?$$ Where $$p=4, q=3$$