Solution of the differential equation `(dy)/(dx)+y/x=sinx` is a. `x(y+cosx)=sinx+C` b. `x(y-cosx)=sinx+C` c. `x(y+cosx)=cos x+C` d. None of these

Explanation

To solve the differential equation \(\frac{dy}{dx} + \frac{y}{x} = \sin x\), we will follow these steps:

### Step 1: Identify the form of the differential equation
The given equation is in the standard form of a first-order linear differential equation:
\[ \frac{dy}{dx} + p(x)y = q(x) \]
where \(p(x) = \frac{1}{x}\) and \(q(x) = \sin x\).
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