# Solve the differential equation dy/dx -y =e^x - Mathematics and Statistics

Sum

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

#### Solution

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.

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