The order and degree of the differential equation -4- dy - dx 2-2 - 3- d 2 y - d x 2 areA- 2-2B- 3-3C- 2-3D- 3-2

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Degree of a Differential Equations

The order and...

Question

The order and degree of the differential equation ${[4 + {(\frac{d y}{d x})}^{2}]}^{2 / 3} = \frac{d^{2} y}{d x^{2}}$ are

2,2

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3,3

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2,3

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3,2

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Solution

The correct option is C
2,3

Here power on the differential coefficient is fractional, therefore change it into positive integer, so
${[4 + {(\frac{d y}{d x})}^{2}]}^{2 / 3} = \frac{d^{2} y}{d x^{2}} \Rightarrow {[4 + {(\frac{d y}{d x})}^{2}]}^{2} = {[\frac{d^{2} y}{d x^{2}}]}^{3}$
Hence order is 2 and degree is 3.

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The correct option is C 2,3Here power on the differential coefficient is fractional, therefore change it into positive integer, so [4+(dydx)2]2/3=d2ydx2⇒[4+(dydx)2]2=[d2ydx2]3 Hence order is 2 and degree is 3.

The order and degree of the differential equation ${[4 + {(\frac{d y}{d x})}^{2}]}^{2 / 3} = \frac{d^{2} y}{d x^{2}}$ are