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प्रश्न
Solve the differential equation `x dy/dx + y = x cos x + sin x`, given that y = 1 when `x = pi/2`
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उत्तर
The given differential equation is
`x dy/dx + y = x cos x + sin x`
`=> dy/dx + y/x = (x cos x + sin x)/x`
This is a linear differential equation of the form `dy/dx + Py = Q`
Thus, the particular solution of the given differential equation is y = sinx.
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