Question

Ques. Determine the order and degree of the differential equation:
cos x dx + cos y dy = 0
plz solve ⚡​

Answer 1

SOLUTION

TO DETERMINE

The order and degree of the differential equation:

$\sf{ \cos x \: dx + \cos y \: dy = 0}$

CONCEPT TO BE IMPLEMENTED

Differential Equation

A differential equation is an equation which involves differential coefficients or differentials

Order of Differential equation

The order of a differential equation is the order of the highest derivative appearing in it.

Degree of Differential equation

The degree of a differential equation is the degree of the highest derivative occuring in it after the equation has been expressed in a form free from radicals and fractions as far as the derivatives are concerned

Solution of Differential equation

A solution of a differential equation is a relation between the variables which satisfies the given differential equation.

The general Solution of a differential equation is that in which the number of arbitrary constants is equal to the order of the differential equation.

EVALUATION

Here the given differential equation is

$\sf{ \cos x \: dx + \cos y \: dy = 0}$

The above differential equation can be rewritten as

$\sf{ \cos x \: dx + \cos y \: dy = 0}$

$\displaystyle \sf{ \implies \: \cos y \: \frac{ dy}{dx} + \cos x = 0 }$

In the above differential equation the order of the highest derivative appearing in it is 1

∴ Order of the differential equation is 1

Also in the differential equation the degree of the highest derivative occuring in it is 1

∴ Degree of the differential equation is 1

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