Which of the following equations is non-linea | vedclass

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(B) differential equation is called linear if the dependent variable and its derivatives occur only in the first degree and are not multiplied togethe

Vedclass · Accepted Answer

$y\frac{dy}{dx} + 4x = 0$

Vedclass · Answer

(B) differential equation is called linear if the dependent variable and its derivatives occur only in the first degree and are not multiplied together. In option $A$,$\frac{dy}{dx} + \frac{y}{x} = \log x$ is linear because the dependent variable $y$ and its derivative $\frac{dy}{dx}$ are in the first degree and not multiplied. In option $B$,$y\frac{dy}{dx} + 4x = 0$,the dependent variable $y$ is multiplied by its derivative $\frac{dy}{dx}$,making it non-linear. In option $C$,$dx + dy = 0$ can be written as $1 + \frac{dy}{dx} = 0$,which is linear. In option $D$,$\frac{dy}{dx} = \cos x$ is linear as the derivative is in the first degree. Therefore,the correct option is $B$.

Which of the following equations is non-linear?

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