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3. Consider the ODE (a) Find the two-term perturbation solution ya(t). Hint: Expand sin(€y) as a Taylor series around 0. (b) Solve the original ODE with € = 0 and show that Ya (t) approaches this solution as € 0. Marks: 7 4. The two-term perturbation solution to y" = €3², y(0)=0, = 3/(0)=2 = on the interval [0,1] is (a) Find the residual re(ya). (b) Show that the residual converges uniformly to 0 on [0,1]. Marks: 4

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