Which one of the following is a linear differ | vedclass

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(D) The standard form of a linear differential equation is $\frac{d y}{d x} + P(x)y = Q(x)$ or $\frac{d x}{d y} + P(y)x = Q(y)$,where $P$ and $Q$ are

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$x^2 d y+x y d x-1=0$

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(D) The standard form of a linear differential equation is $\frac{d y}{d x} + P(x)y = Q(x)$ or $\frac{d x}{d y} + P(y)x = Q(y)$,where $P$ and $Q$ are functions of the independent variable only.Let us analyze option $(D)$:$x^2 d y + x y d x - 1 = 0$Dividing by $d x$:$x^2 \frac{d y}{d x} + x y - 1 = 0$$x^2 \frac{d y}{d x} + x y = 1$Dividing by $x^2$:$\frac{d y}{d x} + \frac{1}{x} y = \frac{1}{x^2}$This is in the form $\frac{d y}{d x} + P(x)y = Q(x)$,where $P(x) = \frac{1}{x}$ and $Q(x) = \frac{1}{x^2}$.Thus,option $(D)$ is a linear differential equation.

Which one of the following is a linear differential equation?

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