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12. Determine order and degree (if defined) of differential equations:
y' + y = e^x

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

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13. Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0

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14. Determine order and degree (if defined) of differential equations:
y″ + 2y′ + sin y = 0

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15.

For each of the differential equations given below, indicate its order and degree (if defined).
$fraction numerator straight d squared straight y over denominator dx squared end fraction plus 5 straight x open parentheses dy over dx close parentheses squared minus 6 straight y space equals space log space straight x$

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16.

For each of the differential equations given below, indicate its order and degree (if defined).
$open parentheses dy over dx close parentheses cubed minus 4 open parentheses dy over dx close parentheses squared plus 7 straight y equals space sin space straight x$

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17.

For each of the differential equations given below, indicate its order and degree (if defined).
$fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction minus sin open parentheses fraction numerator straight d cubed straight y over denominator dx cubed end fraction close parentheses space equals 0$

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18. Find the order and degree of the differential equation

straight x dy over dx plus fraction numerator 3 over denominator begin display style dy over dx end style end fraction equals straight y squared

state also if this is linear or non-linear.

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19.

Find the order and degree of the equation y = px + $square root of straight a squared straight p squared plus straight b squared end root$ when $straight p space equals space dy over dx.$
State also if this is linear or non-linear.

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20.

Determine the order and degree of the differential equation:
$open square brackets 1 plus open parentheses dy over dx close parentheses squared close square brackets to the power of 3 over 2 end exponent space equals 5 fraction numerator straight d squared straight y over denominator dx squared end fraction$