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