Which of the following equations is a linear | vedclass

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Question

(C) differential equation is linear if the dependent variable $y$ and its derivatives appear only in the first degree and are not multiplied together.

Vedclass · Accepted Answer

$\frac{dy}{dx} + \frac{y}{x} = \log x$

Vedclass · Answer

(C) differential equation is linear if the dependent variable $y$ and its derivatives appear only in the first degree and are not multiplied together.In option $A$,the term $(\frac{d^2y}{dx^2})^2$ has a degree of $2$,so it is non-linear.In option $B$,the term $\sqrt{1 + (\frac{dy}{dx})^2}$ makes the equation non-linear because the derivative is inside a square root.In option $C$,$\frac{dy}{dx} + \frac{y}{x} = \log x$ is of the form $\frac{dy}{dx} + Py = Q$,where $P = \frac{1}{x}$ and $Q = \log x$. This is a linear differential equation.In option $D$,the term $y\frac{dy}{dx}$ involves the product of the dependent variable and its derivative,making it non-linear.Therefore,the correct option is $C$.

Which of the following equations is a linear differential equation?

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