The differential equation frac{d^3y}{dx^3}-5y | vedclass

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(B) differential equation is said to be linear if the dependent variable $y$ and its derivatives occur only in the first degree and are not multiplied

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Non-linear equation of degree $1$

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(B) differential equation is said to be linear if the dependent variable $y$ and its derivatives occur only in the first degree and are not multiplied together.In the given equation $\frac{d^3y}{dx^3}-5y \frac{dy}{dx}+xy=0$,the term $y \frac{dy}{dx}$ involves the product of the dependent variable $y$ and its derivative $\frac{dy}{dx}$.Because of this product,the equation is non-linear.The order of the highest derivative $\frac{d^3y}{dx^3}$ is $3$.The degree of the highest derivative is $1$.Therefore,it is a non-linear differential equation of order $3$ and degree $1$.

The differential equation $\frac{d^3y}{dx^3}-5y \frac{dy}{dx}+xy=0$ represents :-

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