The degree of the differential equation- d3ydx3-3d2ydx2-x2logd3ydx3is-

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Order of a Differential Equation

The degree of...

Question

The degree of the differential equation
$\frac{d^{3} y}{d x^{3}} + 3 \frac{d^{2} y}{d x^{2}} = x^{2} log \frac{d^{3} y}{d x^{3}}$ is:

1

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2

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3

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none of these

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Solution

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{[2 \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2}]}^{3 / 2} = (\frac{d^{3} y}{d x^{3}})

{[1 + {(\frac{d y}{d x})}^{2}]}^{5 / 2} = \frac{d^{3} y}{{d x}^{3}}

{(\frac{d^{3} y}{d x^{3}})}^{\frac{2}{3}} + 4 - 3 \frac{d^{2} y}{d x^{2}} + 5 \frac{d y}{d x} = 0

{(\frac{d^{3} y}{d x^{3}})}^{\frac{3}{2}} + {(\frac{d^{3} y}{d x^{3}})}^{\frac{- 2}{3}} = 0

m

n

{(\frac{d^{2} y}{d x^{2}})}^{5} + 4 \frac{(\frac{d^{2} y}{d x^{2}})}{(\frac{d^{3} y}{d x^{3}})} + (\frac{d^{3} y}{d x^{3}}) = x^{2} - 1

(m, n) =

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