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Differential Equations

Short Answer Type

41. For problem given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation:

straight x squared space equals space 2 straight y squared space log space straight y

left parenthesis straight x squared plus straight y squared right parenthesis space dy over dx minus straight x space straight y space equals space 0

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Multiple Choice Questions

42. The number of arbitrary constants in the general solution of a differential equation of fourth order are:

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43.

The number of arbitrary constants in the particular solution of a differential equation of third order are

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Short Answer Type

44. Find the differential equation that will represent the family of straight lines y = m x + c, where m, c (∈ R) are parameters.

The equation of the family of lines is
y = mx + c
$therefore space space space space space space space space space dy over dx space equals space straight m$
Again differentiating w.r.t. 'x' we get,
$fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space 0$
This is required differential equations.