The order and degree of the differential equa | vedclass

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Question

(C) Given the differential equation: $\frac{d^2 y}{d x^2} = \sqrt{\frac{d y}{d x}}$To find the degree,we must eliminate the radical sign by squaring b

Vedclass · Accepted Answer

$2, 2$

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(C) Given the differential equation: $\frac{d^2 y}{d x^2} = \sqrt{\frac{d y}{d x}}$To find the degree,we must eliminate the radical sign by squaring both sides:$\left(\frac{d^2 y}{d x^2}\right)^2 = \frac{d y}{d x}$The order of a differential equation is the highest derivative present,which is $2$ (from $\frac{d^2 y}{d x^2}$).The degree of a differential equation is the power of the highest order derivative after the equation is made free from radicals and fractions. Here,the power of $\frac{d^2 y}{d x^2}$ is $2$.Therefore,the order is $2$ and the degree is $2$.

The order and degree of the differential equation $\frac{d^2 y}{d x^2}=\sqrt{\frac{d y}{d x}}$ are respectively

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