Continuity and Differentiability
If y=500e7x+600e−7x, show that dx2d2y=49y
Find the particular solution of differential equation xsin2xy−ydx+xdy=0, it being given that y=4π when x=1
If x and y are connected parametrically by the equations given, without eliminating the parameter, Find dxdy.
A curve passes through the point (0,−2) and at any point (x,y) of the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point. Find the equation of the curve.