The degree and the order of the differential | vedclass

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(A) Given differential equation is: $\frac{d^{2} y}{d x^{2}}=\sqrt[3]{1+\left(\frac{d y}{d x}\right)^{2}}$To find the degree,we must eliminate the rad

Vedclass · Accepted Answer

$3$ and $2$

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(A) Given differential equation is: $\frac{d^{2} y}{d x^{2}}=\sqrt[3]{1+\left(\frac{d y}{d x}\right)^{2}}$To find the degree,we must eliminate the radical. Cube both sides of the equation:$\left(\frac{d^{2} y}{d x^{2}}\right)^{3} = 1 + \left(\frac{d y}{d x}\right)^{2}$The order of a differential equation is the highest derivative present. Here,the highest derivative is $\frac{d^{2} y}{d x^{2}}$,so the order is $2$.The degree of a differential equation is the power of the highest derivative when the equation is expressed as a polynomial in derivatives. Here,the power of $\frac{d^{2} y}{d x^{2}}$ is $3$,so the degree is $3$.Therefore,the degree is $3$ and the order is $2$.

The degree and the order of the differential equation $\frac{d^{2} y}{d x^{2}}=\sqrt[3]{1+\left(\frac{d y}{d x}\right)^{2}}$ respectively are

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