FP2.5 - Second order differential equations

The linear second order differential The auxiliary equation may have real distinct, equal or d2y dy complex roots. f(x) will have one of the forms equation a + b + cy = f(x) dx2 dx k epx, A + Bx, p + qx + cx2 or m cos ωx + n sin ωx. where a, b and c are real constants Students should be familiar with the terms ‘complementary and the particular integral can be function’ and ‘particular integral’. found by inspection or trial.; Students should be able to solve equations of the form d2y + 4y = sin 2x. dx2.

Use fp2.5.1 - linear second order differential to connect the rule to the data and decision in the question.

This matters because fp2.5.1 - linear second order differential determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp2.5.1 - linear second order differential to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP2.5.1 - Linear second order 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 fp2.5.2 - reducible second order differential equations to connect the rule to the data and decision in the question.

This matters because fp2.5.2 - reducible second 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 fp2.5.2 - reducible second 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.