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Formation of a Differential Equation from a General Solution

Degree of D.E...

Question

Degree of D.E ${[5 + {(\frac{d y}{d x})}^{2}]}^{3 / 2} = 6 \frac{d^{2} y}{d x^{2}}$

A

1

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B

2

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C

3

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D

6

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Solution

The correct option is A $2$
The order of a differential equation is the order of the highest order derivative present in the equation.
The degree of a differential equation is the power of the highest order derivative in the equation.

${(5 + {(\frac{d y}{d x})}^{2})}^{\frac{3}{2}} = 6 \frac{d^{2} y}{d x^{2}}$
Squaring on both sides
${(5 + {(\frac{d y}{d x})}^{2})}^{3} = {(6 \frac{d^{2} y}{d x^{2}})}^{2}$

Highest order derivative is $\frac{d^{2} y}{d x^{2}}$ in the above polynimial equation and its power is $2$ .
Degree is $2.$

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Similar questions

Q. The degree of D.E

{[5 + {(\frac{d y}{d x})}^{2}]}^{5 / 3} = 7 (\frac{d^{2} y}{d x^{2}})

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

Q. Degree of D.E. of

y = x \frac{d y}{d x} - \sqrt{1 + {(\frac{d y}{d x})}^{2}}

Q. Order and degree of the D.E

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

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

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