The order and degree of D-E - 1-d3ydx3 -1-3-d2ydx2 is-

The correct option is B 3, 1 (1+y_3)^1/3=y_2 ⇒ 1+y_3=y_2^3 ⇒ order=3 degree=1 ...

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Degree of a Differential Equations

The order and...

Question

The order and degree of D.E ${[1 + \frac{d^{3} y}{d x^{3}}]}^{1 / 3} = \frac{d^{2} y}{d x^{2}}$ is:

3, 1

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4, 1

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3, 2

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3, 3

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Solution

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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) =

m

n

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

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

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

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

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