The difference of the order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^{-\frac{7}{2}}\left(\frac{d^3 y}{d x^3}\right)^2-\left(\frac{d^2 y}{d x^2}\right)^{-\frac{5}{2}}\left(\frac{d^4 y}{d x^4}\right)=0$ is

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Aicharya · Accepted Answer

Given differential equation $\begin{aligned} & \left(\frac{d^2 y}{d x^2}ight)^{-\frac{7}{2}} \cdot\left(\frac{d^3 y}{d x^3}ight)^2-\left(\frac{d^2 y}{d x^2}ight)^{-\frac{5}{2}} \cdot\left(\frac{d^4 y}{d x^4}ight)=0 \ & \Rightarrow\left(\frac{d^2 y}{d x^2}ight)^{-7} \cdot\left(\frac{d^3 y}{d x^3}ight)^4-\left(\frac{d^2 y}{d x^2}ight)^{-5} \cdot\left(\frac{d^4 y}{d x^4}ight)^2=0 \ & \Rightarrow\left(\frac{d^3 y}{d x^3}ight)^4 \cdot\left(\frac{d^2 y}{d x^2}ight)^5-\left(\frac{d^2 y}{d x^2}ight)^7 \cdot\left(\frac{d^4 y}{d x^4}ight)^2=0 \end{aligned}$ So, order $=4$, degree $=2$ Now, order - degree $=4-2=2$.

The difference of the order and degree of the differential equation $\left(\frac{d^2 y}{d…

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