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Well, I know that in linear differential equation the variable and its derivatives are raised to power of $1$ or $0$. But I am confused where did the standard form of linear differential equation came form?

That is, why is the equation $dy/dx + P(x)y=Q(x)$ said to be standard form?

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    Because someone decided they liked writing the equations that way, and it stuck. – 2017-02-15
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    but there must be some reason behind it ? some similarities with other equations ? or something? – 2017-02-15
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    What are the alternatives with only two functions; $P(x)y'(x) + Q(x)y = 1$ and $P(x)y'(x) + y = Q(x)$ right. On this form it's not guaranteed to be an acctual ODE (we could have $P(x) = 0$). We would then have to add $P\not = 0$ as a requirement. This is similar to when we sometimes choose to write $f(x) = x^n + a_{n-1}x^{n-1} + \ldots + a_1 x + a_0$ for a $n$'th order polynomial. This guarantees that it's of order $n$. On this form it's also easy to remember the integrating factor: it's simply $e^{\int P(x){\rm d}x}$. Anyway, the real answer here is what Arthur said about. – 2017-02-15
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    @Winther Yeah I got it, your comment was really helpful to dig my past knowledge. – 2017-02-15

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The standard form of a differential equation is ‎$$f_n\frac{d^ny}{dx^n}+f_{n-1}\frac{d^{n-1}y}{dx^{n-1}}+\cdots+f_1\frac{dy}{dx}+f_0y=g$$‎ for $n=1$, this called differential equation of the first order, i.e. ‎$$f_1\frac{dy}{dx}+f_0y=g$$‎ you take ‎$$\frac{dy}{dx}+py=q$$‎ while $p$ and $q$ are continuous functions of $x$, this called linear differential equation of the first order.

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    That's what I was looking for . Can you please tell me where did you got that knowledge form? – 2017-02-15
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    @rpawp With intuition you can always find something. – 2017-02-15
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    okay I am now enlightened! – 2017-02-15