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प्रश्न
Find the general solution of the differential equation `dy/dx - y = sin x`
उत्तर
The given differential equation is
`dy/dx - y = sin x` .....(1)
Clearly, it is a linear differential equation of the form `dy/dx + Py=Q`
Here
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Solution: `dy/dx+2xy=x` ...(1)
This is the linear differential equation of the form `dy/dx +Py =Q,"where"`
`P=square` and Q = x
∴ `I.F. = e^(intPdx)=square`
The solution of (1) is given by
`y.(I.F.)=intQ(I.F.)dx+c=intsquare dx+c`
∴ `ye^(x^2) = square`
This is the general solution.
