Question

Use the methods of section 8.3 to find the general solutions of the given systems of differential equations in the following two problems. 4. = X-1 5. dx dt dy dt dx =x+3y + 1 dt dy = x - y - 1 dt x + 2y

Answer 1

G빼 ig dre dt system of differential equations 앵 번 - 1 dy at 개42y

0 il a sisat order Isot degree lineas differential equation, dre -x=-/ 8 at ftat gutegrating factor Solution of S-1. et alt =ēt ie ē . fc t net е tci belti = It get dy -24 at e using this in e - 1-ciet f-2ct est Butysating factor and solution of 4 ezt y = f(--ciet) ezt dt + G SC - ppt - ciet) at the I eat + ciet yetl= t get toest - -2t y tą 기 2

- Therefore, relt= fl cet cet + cze2t + 1 YCH = ie, at 0 CI et to + alth yeth al @ (62) 1/2) - -
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