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# hw6 - y and any constant c(Hint just plug and chug 2...

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MAT22B–1: HW 6 ————————————————————————————————————————— Do Problems #8, 18 in § 3.6; Problems # 6, 7, 10 in § 3.7; and 1. In lecture we defined the second order differential operator L = D 2 + pD + q, where p ( t ) and q ( t ) are continuous. In other words, Ly = D 2 y + pDy + qy = y + p ( t ) y + q ( t ) y. Show that L is a linear operator, i.e, show L satisfies (i) L [ y 1 + y 2 ] = Ly 1 + Ly 2 , for any two twice differentiable functions y 1 and y 2 . (ii) L [ cy ] = cLy,
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Unformatted text preview: y and any constant c. (Hint: just plug and chug) 2. Consider the following nonhomogeneous ODE y 00 + 3 y = 2 t 4 + t 2 e-3 t + sin 3 t. (i) Find the general solution. (ii) Determine if the ODE is stable or unstable. If stable, identify the stable solution. A table of basic integrals (with proofs) can be found online at http://math2.org/math/integrals/tableof.htm 1...
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