The degree of the differential equation 3frac | vedclass

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(B) Given the differential equation: $3\frac{d^2y}{dx^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}$ To find the degree,we must elimi

Vedclass · Accepted Answer

$2$

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(B) Given the differential equation: $3\frac{d^2y}{dx^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}$ To find the degree,we must eliminate the fractional exponent by squaring both sides: $\left( 3\frac{d^2y}{dx^2} \right)^2 = \left[ \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2} \right]^2$ $9\left( \frac{d^2y}{dx^2} \right)^2 = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^3$ The highest order derivative present in the equation is $\frac{d^2y}{dx^2}$,which is of order $2$. The power (exponent) of the highest order derivative after making the equation a polynomial in derivatives is $2$. Therefore,the degree of the differential equation is $2$.

The degree of the differential equation $3\frac{d^2y}{dx^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}$ is

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