Continuity and Differentiability
The solution of the D.E. cosx(1+cosy)dx−siny(1+sinx)dy=0 is
Find a particular solution satisfying the given condition for the following differential equation.
xdxdy−y=logx, given that y=0 when x=1.
Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.
Show that the function f defined by f(x)=∣1−x+x∣, where x is any real number, is a continuous function.