Question

Solve the differential equation `dy/dx -y =e^x`

Answer 1

`dy/dx -y =e^x`

The given equation is of the form `dy/dx+Py=Q`

Where, `P=-1 and Q=e^x`

`I.F=e^(intpdx)=e^(int-1dx)=e^-x`

Solution of the given equation is

`y(I.F)=intQ(I.F) dx +c`

`y.e^-x=inte^x.e^-xdx+c`

`ye^-x=x+c`

we get c = 1

`y.e^(-x)=x+1`

`y = (x + 1) e^x` is a particular solution of D.E.