If m and n are the order and degree of the di | vedclass

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(D) The given differential equation is $\left( \frac{d^2y}{dx^2} \right)^5 + 4\frac{\left( \frac{d^2y}{dx^2} \right)^3}{\left( \frac{d^3y}{dx^3} \righ

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$m = 3$ and $n = 2$

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(D) The given differential equation is $\left( \frac{d^2y}{dx^2} \right)^5 + 4\frac{\left( \frac{d^2y}{dx^2} \right)^3}{\left( \frac{d^3y}{dx^3} \right)} + \frac{d^3y}{dx^3} = x^2 - 1$. To find the degree,we must eliminate the fraction by multiplying the entire equation by $\frac{d^3y}{dx^3}$. Multiplying by $\frac{d^3y}{dx^3}$,we get: $\left( \frac{d^2y}{dx^2} \right)^5 \left( \frac{d^3y}{dx^3} \right) + 4\left( \frac{d^2y}{dx^2} \right)^3 + \left( \frac{d^3y}{dx^3} \right)^2 = (x^2 - 1) \left( \frac{d^3y}{dx^3} \right)$. The highest order derivative present in the equation is $\frac{d^3y}{dx^3}$,so the order $m = 3$. The degree is the power of the highest order derivative after the equation is made a polynomial in derivatives. The highest power of $\frac{d^3y}{dx^3}$ is $2$. Thus,$m = 3$ and $n = 2$.

If $m$ and $n$ are the order and degree of the differential equation $\left( \frac{d^2y}{dx^2} \right)^5 + 4\frac{\left( \frac{d^2y}{dx^2} \right)^3}{\left( \frac{d^3y}{dx^3} \right)} + \frac{d^3y}{dx^3} = x^2 - 1$,then

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