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Differential Equations

Short Answer Type

1. Write the order and degree of the differential equation

open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses squared plus open parentheses dy over dx close parentheses cubed plus 2 straight y space equals space 0

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2. Find the order and degrees, if defined, of each of the following differential equations:

dy over dx minus cosx space equals 0

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3. Find the order and degrees, if defined, of each of the following differential equations:

straight x space straight y space fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared minus straight y dy over dx space equals space 0

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4. Find the order and degrees, if defined, of each the following differential equations:

straight y to the power of straight m plus straight y squared plus straight e to the power of straight y space equals space 0

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5. Determine order and degree (if defined) of differential equations:

fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction plus sin left parenthesis straight y to the power of straight m right parenthesis space equals space 0

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6. Determine order and degree (if defined) of differential equations:
$straight y apostrophe plus 5 space straight y equals 0$

The given differential equation is
y' + 5 y = 0
The highest order derivative present in the given differential equation is y' and index of its highest power is one.
∴ the given differential equation is of order 1 and degree 1.

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7. Determine order and degree (if defined) of differential equations:

open parentheses ds over dt close parentheses to the power of 4 plus 3 straight s fraction numerator straight d squared straight s over denominator dt squared end fraction equals 0

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8. Determine order and degree (if defined) of differential equations:

open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses squared plus cos open parentheses dy over dx close parentheses space equals space 0

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9. Determine order and degree (if defined) of differential equations:

fraction numerator straight d squared straight y over denominator dx squared end fraction equals cos space 3 straight x plus space sin space 3 straight x

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10. Determine order and degree (if defined) of differential equations:

left parenthesis straight y to the power of straight m right parenthesis squared plus left parenthesis straight y to the power of straight m right parenthesis cubed plus left parenthesis straight y apostrophe right parenthesis to the power of 4 plus straight y to the power of 5 space equals space 0

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