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Solve the Differential Equation `X Dybydx + Y = X Cos X + Sin X`, Given that Y = 1 When `X = Pi by 2 - Mathematics

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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Solution

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 sinx.

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