Write the degree of the differential equation- dydx4-3xd2ydx2-0-

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Degree of a Differential Equations

Write the deg...

Question

Write the degree of the differential equation:
$(\frac{d y}{d x})^{4} + 3 x \frac{d^{2} y}{d x^{2}} = 0$ .

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Solution

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

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

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

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

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

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