Let y(t) = (y1(t), y2(t))^T and(adsbygoogle = window.adsbygoogle || []).push({});

A(t) = (a(t) b(t)

c(t) d(t)).

A(t) is a 2x2 matrix with a,b,c,d all polynomials in t. Consider the two dimensional Cauchy problem y'(t) = A(t)y(t), y(0)=y0.

Show that a solution exists for all t>=0.

Give a general condition on the A(t) which ensures global existence.

Please could you help me with this question - I don't know what to do. I need to use Picard somewhere I think but I don't know how to go about it.

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# Two dimensional Cauchy problems

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