The order and degree of the differential equa | vedclass

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

Vedclass · Accepted Answer

$2, 3$

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(B) Step $1$: Given equation is $\sqrt{1 + \frac{1}{(dy/dx)^2}} = (d^2y/dx^2)^{3/2}$.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 can be written as $\frac{\sqrt{1 + (dy/dx)^2}}{|dy/dx|} = (d^2y/dx^2)^{3/2}$.Step $4$: Square both sides to remove the square root on the right side: $\frac{1 + (dy/dx)^2}{(dy/dx)^2} = (d^2y/dx^2)^3$.Step $5$: Multiply by $(dy/dx)^2$ to clear the fraction: $1 + (dy/dx)^2 = (dy/dx)^2 \cdot (d^2y/dx^2)^3$.Step $6$: The highest order derivative present is $d^2y/dx^2$, so the order is $2$.Step $7$: The power of the highest order derivative after making the equation a polynomial in derivatives 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, respectively:

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