1 answer

Differential Equations. Can someone show a more detailed solution? Having a bit of trouble understanding how to get there with

Question:

8. Assume that Xi (t) = (t, 1)T and X2(t) = (t2, 2t) are solutions of a 2x 2 linear system X, P (t) X of differential equati

Differential Equations. Can someone show a more detailed solution? Having a bit of trouble understanding how to get there with the provided solution.

8. Assume that Xi (t) = (t, 1)T and X2(t) = (t2, 2t)" are solutions of a 2x 2 linear system X, P (t) X of differential equations. The Wronskian of Xi and X2 equals t showing that Xi and X2 form a fundamental set of solutions on interval(s) o,0)U(0,00) There is a unique solution of X P(t) with X (-2) -(3,0) on the maximal interval00,0) Solution. det 2which is non-zero exactly on (-,0)0(0,o).

Answers

Solution:

2 (2 Shouing e x1 and x, from a -fundamental set 얌 soluton on atena Isr_{。 2

.

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