FP2.4 - First order differential equations

Further solution of first order The formation of the differential equation may be required. differential equations with Students will be expected to obtain particular solutions and separable variables. also sketch members of the family of solution curves.

Use fp2.4.1 - further solution of first order to connect the rule to the data and decision in the question.

This matters because fp2.4.1 - further solution of first order determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp2.4.1 - further solution of first order to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP2.4.1 - Further solution of first order is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

First order linear differential The integrating factor e ∫Pdx may be quoted without proof. dy equations of the form + Py = Q dx where P and Q are functions of x.

Use fp2.4.2 - first order linear differential to connect the rule to the data and decision in the question.

This matters because fp2.4.2 - first order linear differential determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp2.4.2 - first order linear differential to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP2.4.2 - First order linear differential is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Differential equations reducible to the above types by means of a given substitution.

Use fp2.4.3 - reducible first order differential equations to connect the rule to the data and decision in the question.

This matters because fp2.4.3 - reducible first order differential equations determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp2.4.3 - reducible first order differential equations to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.