Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.(i) y=aex+be−x+x2 : xdx2d2y+2ydxdy−xy+x2−2=0
Show that the family of curves for which the slope of the tangent at any point (x, y) on it is 2xyx2+y2, is given by x2−y2=cx.
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.y=ae3x+be−2x
The differential equations, find a particular solution satisfying the given condition: (1+x2)dxdy+2xy=1+x21;y=0when x=1
Find the equation of a curve passing through the point (0, 0) and whose differentialequation is yprime=exsinx
Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.
Show that the general solution of the differential equation dxdy+x2+x+1y2+y+1=0 is given by (x+y+1)=A(1−x−y−2xy) where A is a parameter