Assertion and reason

Exercise and reference answers

Questions

1. Reason

   Degree is defined only when the equation is polynomial in its derivatives.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Some differential equations have no degree.

2. Reason

   A general solution carries as many constants as the order.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   A second order equation has two arbitrary constants in its general solution.

3. Reason

   Separation requires the x and y terms to split completely.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   Every differential equation can be solved by separating variables.

4. Reason

   It carries no arbitrary constants left to vary.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   A particular solution names one curve.

Explanation