Question

The no. of arbitrary constant in the general solution of a differential equation of 3rd order is

Answer 1

Answer:

The number of arbitrary constants in the general solution of a differential equation is 3

Step-by-step explanation:

In this question,

Let y''' = 1

On integrating we get,

y'' = x + A                        where A is the constant

Now , again Integrating we get,

y' = $\frac{x^{2}}{2}\ +\ A\ +\ B$              where A and B are constant.

Integrating again,

y = $\frac{x^{3}}{6}\ +\ A\ +\ B\ +\ C$         Where A, B, and C are constants

Therefore, Number of Constants = 3

Hence, Number of arbitrary constants in a general solution of a differential equation is 3

Answer 2

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CONCEPT TO BE IMPLEMENTED

DIFFERENTIAL EQUATION

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

ORDER OF A DIFFERENTIAL EQUATION

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

DEGREE OF A 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 A DIFFERENTIAL EQUATION

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

RELATION BETWEEN ORDER OF A DIFFERENTIAL EQUATION & ARBITRARY CONSTANTS

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.

TO DETERMINE

The number of arbitrary constant in the general solution of a differential equation of 3rd order

CALCULATION

Since the differential equation is of 3rd order

Hence the number of arbitrary constant in the general solution of a differential equation of 3rd order is 3

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LEARN MORE FROM BRAINLY

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