Continuity and Differentiability
If y=Aemx+Benx, show that dx2d2y−(m+n)dxdy+mny=0
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.
Find the particular solution of the following differential equation:
secy(1+x2)dy+2xtanydx=0, given that y=4π, when x=1.
Find the equation of a curve which passes through the origin and whose differential equation is dxdy=exsinx.