Edexcel A-Level Mathematics A2 Fp2 5 1 Linear Second Order Differential Questions

Practise Edexcel IAL FP2.5.1 by solving auxiliary equations, forming complementary functions, comparing coefficients and stating general solutions.

Exam points

solve auxiliary equations with real, repeated or complex roots to form the CF
construct a particular integral by coefficient comparison and state the general solution

[Maximum number: 5]

Solve differential equation (II) to determine y in terms of t.

For the complementary function,

m^2-m-2=0

so m=2,-1 and

y=Ae^{2t}+Be^{-t}

For a particular integral, let $y=at^2+bt+c$ . Then

\frac{dy}{dt}=2at+b,\qquad \frac{d^2y}{dt^2}=2a

Substitution gives

2a-2at-b-2at^2-2bt-2c=1+4t-2t^2

Comparing coefficients:

a=1,\qquad b=-3,\qquad c=2

Therefore

y=Ae^{2t}+Be^{-t}+t^2-3t+2

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