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Differential Equations

Short Answer Type

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

straight y to the power of straight m plus 2 straight y to the power of straight n plus straight y apostrophe space equals space 0

91 Views

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

98 Views

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

99 Views

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

105 Views

15.

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

124 Views

16.

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

89 Views

17.

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

91 Views

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.

156 Views

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.

The given equation is
$straight y equals px plus square root of straight a squared straight p squared plus straight b squared end root space space space or space space space space space space space straight y minus straight p space straight x space space equals square root of straight a squared straight p squared plus straight b squared end root$
or $left parenthesis straight y minus px right parenthesis squared space equals straight a squared straight p squared plus straight b squared$ or $straight y squared plus straight p squared straight x squared space minus space 2 space pxy space equals straight a squared straight p squared plus straight b squared$
or $straight y squared plus straight x squared open parentheses dy over dx close parentheses squared minus 2 xy dy over dx space equals space straight a squared open parentheses dy over dx close parentheses squared plus straight b squared$
It is of order 1, degree 2 and non-linear

212 Views

20.

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

104 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

19. Find the order and degree of the equation y = px + when State also if this is linear or non-linear.

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.