Which of the following equations is non-linea | vedclass

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(D) 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

$x\frac{dy}{dx} + \frac{3}{dy/dx} = y^2$

Vedclass · Answer

(D) differential equation is linear if the dependent variable $y$ and its derivatives appear only in the first degree and are not multiplied together.For option $(d)$,we have $x\frac{dy}{dx} + \frac{3}{dy/dx} = y^2$.Multiplying both sides by $\frac{dy}{dx}$,we get $x\left(\frac{dy}{dx}\right)^2 - y^2\frac{dy}{dx} + 3 = 0$.Since the degree of the derivative $\frac{dy}{dx}$ is $2$,this differential equation is non-linear.

Which of the following equations is non-linear?

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