Question

5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of parameters equations that have to be satisfied to for rt)X(ut) to h such that yn(x) = cvitc2U2, where ci and c2 are constant. and z2 y corresponding to the system found in (b). (As a result, X(t)-2) is a fundamental matrix for the same homogeneous system). v(t)ua(t) to a particular solution of the nonhomogeneous second order ODE. a particular solution of the nonhomogeneous system of ODE found in (L) (G) Use the definition of al and a2 in (c) to show that the s ystems of equations found in (d) and the equations found in (e) are equivalent.

Answer 1

arn Systeniven b 지_n2. dit 2lt) 3 2t using (b) 2ヒ 2019-5-3 03:01

and Simte t ง(t)-ul, c" 22는 u2 チ3 estu i t u2e2.tt e 1 3 1 2t let ri 26f 2ヒ 3 ①and E) 2 (342) 2と e Cte 2019-5-3 03:01
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