Show that `y=Ce^-x` is a solution of the differential equation `dy/dx+y=0`.

The general solution of the differential equation (y dx - x dy)/y=0 .

Show that the general solution of the differential equation (dy)/(dx)+(y^2+y+1)/(x^2+x+1)=0 is given by ((x+y)+1)=A(1-x-y-2 x y) , where A is parameter.

The solution of the differential equation (dy)/(dx)= 1/(x+y^2) is

Show that the function y=Ax+B/x is a solution of the differential equation x^2(d^2y)/dx^2+xdy/dx-y=0 .

Check whether y=e^(-3x) is a solution of the differential equation frac(d^2y)(dx^2)+frac(dy)(dx)-6y=0

The solution of the differential equation x(dy)/(dx)=(y)/(1+logx) is

The general solution of the differential equation (dy)/(dx)=e^(x+y) is

Find the general solution of the differential equation (dy)/(dx)-y=cos x .

Consider the differential equation x(d^2y)/dx^2+2dy/dx-xy+x^2-2=0 .Show that xy=ae^x+be^-x+x^2 is a solution of the given equation.