A. Singular solution contains no arbitrary constants.
B. Singular solution can be obtained from complete primitive.
a)
A is true, B is false
b)
Both A and B are true
c)
Both A and B are false
d)
None of the above
Correct answer is option 'B'. Can you explain this answer?

Question

A. Singular solution contains no arbitrary constants.
B. Singular solution can be obtained from complete primitive.

a)
A is true, B is false
b)
Both A and B are true
c)
Both A and B are false
d)
None of the above

Correct answer is option 'B'. Can you explain this answer?

Answer

Singular Solution and Arbitrary Constants

Definition:
A singular solution is a solution to a differential equation that cannot be obtained from the general solution by assigning values to the arbitrary constants.

Explanation:
A. Singular solution contains no arbitrary constants.
- This statement is true. A singular solution is a solution that does not involve any arbitrary constants. It is a specific solution that satisfies the differential equation without any additional parameters.

B. Singular solution can be obtained from complete primitive.
- This statement is also true. A complete primitive is the general solution to a differential equation that includes all possible solutions by introducing arbitrary constants. By assigning specific values to these constants, we can obtain singular solutions.

Example:
Consider the differential equation:
dy/dx = 2x

The general solution to this differential equation is:
y = x^2 + C

Here, C is an arbitrary constant that can take any value. If we assign a specific value to C, say C = 1, we obtain a singular solution:
y = x^2 + 1

This singular solution satisfies the differential equation dy/dx = 2x without any arbitrary constant.

Conclusion:
In summary, a singular solution does not involve any arbitrary constants and can be obtained from the complete primitive by assigning specific values to the constants. Therefore, both statements A and B are true.

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