The elimination of the arbitrary constants A,B and C from `y=A+Bx+Ce^(-x)` leads to the differential equation.

The elimination of the arbitrary constant k from the equation y=(x+k)e^(-x) gives the differential equation

The differential equation obtained by eliminating the arbitrary constants a and b from xy = ae^(x) + be^(-x) is

By eliminating arbitary constant of equation y = c^2 + c/ x find differential equation .

If the general solution of a differential equation is (y+c)^2=cx , where c is an arbitrary constant then the order of the differential equation is _______.

Eliminating the arbitrary constants B and C in the expression y = (2)/(3C) (C x- 1)^(3/2) + B , we get ,

The differential equation of minimum order by eliminating the arbitrary constants A and C in the equation y = A [sin (x + C) + cos (x + C)] is :

Verify that the function y=c_(1)e^(ax)cos bx+c_(2)e^(ax)sin bx, where c_(1),c_(2) are arbitrary constants is a solution of the differential equation.(d^(2)y)/(dx^(2))-2a(dy)/(dx)+(a^(2)+b^(2))y=0

The general solution of a differential equation is y= ae ^(bx+ c) where are arbitrary constants. The order the differential equation is :