Assertion and reason: forms and methods

Exercise and reference answers

Questions

1. Reason

   That is the defining shape of a first order linear equation.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The linear method needs P and Q to depend on x alone.

2. Reason

   Each form admits a different solution method.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Recognising the form matters before integrating.

3. Reason

   Leibnitz introduced the integral sign in 1675.

   Verdict

   Both are true; the reason does not explain the assertion.

   Assertion

   A differential equation involves derivatives.

Explanation