The order and degree of the differential equation d2y-dx2-1-dy-dx4 are respectively-

The correct option is C 2, 3 Given differential equation is #160; d^2y/dx^2=√(1 (dy/dx)^4) ⇒(d^2y/dx^2)^3 =1 (dy/dx)^4 ∴ Order ...

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Order of a Differential Equation

The order and...

Question

The order and degree of the differential equation $\frac{d^{2} y}{d x^{2}} = \sqrt[3]{1 - {(\frac{d y}{d x})}^{4}}$ are respectively.

2, 3

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3, 2

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2, 4

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2, 2

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Solution

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\frac{d^{2} y}{d x^{2}} = {(\frac{d y}{d x})}^{2}

\frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{1 / 3} + x^{1 / 4} = 0

\frac{d^{2} y}{d x^{2}} = \sqrt[3]{1 + (\frac{d y}{d x})^{4}}

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

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

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