Edexcel IAL Mathematics FP2.5.1 linear second order differential equations

Practise linear second order differential equations by finding the complementary function and a particular integral for f(x).

Exam points

[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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