The order and degree of the differential equa | vedclass

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(A) Step $1$: Write the given equation: $\sqrt{1 + \frac{1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$.Step $2$: Simplify the expression inside the square root:

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Order $2$, Degree $3$

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(A) Step $1$: Write the given equation: $\sqrt{1 + \frac{1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$.Step $2$: Simplify the expression inside the square root: $\sqrt{\frac{(dy/dx)^2 + 1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$.Step $3$: This becomes $\frac{\sqrt{(dy/dx)^2 + 1}}{|dy/dx|} = (d^2y/dx^2)^{3/2}$.Step $4$: Square both sides to remove the square root on the right: $\frac{(dy/dx)^2 + 1}{(dy/dx)^2} = (d^2y/dx^2)^3$.Step $5$: Multiply by $(dy/dx)^2$ to clear the fraction: $(dy/dx)^2 + 1 = (d^2y/dx^2)^3 \cdot (dy/dx)^2$.Step $6$: The highest order derivative is $d^2y/dx^2$, so the order is $2$. The power of the highest order derivative is $3$, so the degree is $3$.

The order and degree of the differential equation $\sqrt{1 + \frac{1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$ are ...

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