## Answers

equation is, 7(0) = -1 Here we use The narod, weget logy. @ The given dy + y =22* 1. the method of variation parameters. reduced equation of (1) is, dy + y = 0. dy -at kagal 061 -y OF, dre 2).

091 y = Geox Dis regarding the constant of integration, we take yrity one of the solutions of the reduced equation het J= ut Verx dy da eredu dre vern Then the equation (1) be comes enn du तर vera thera= 20e 274 or. du din = 2€ Integrating, weget V = 28e24 duta V e2244 Therefore the solution is, y=1e2aeculen = eMaciel 7(0)=rl gives 1+q=-| .4 = -2.

Then the required solution of the equation (1) is, لد e-ze-X. (swer). 12 4 The given equation is, dq +9= Cosat (3), dt The reduced equation of 3) i, dq dt +920 q Gent 9=9 = e-t as the one of the the reduced equation.

.
Sobitions of fet vent 19 - 9 H = ent de vent Tren तस dq Then the equation (3) Cosafi becomes ent du 3 de ellosat Integrating weget eak v=jetloste ec, where cisa arbitrary Constanta we know that de are Cosby = (a cosbx+ b sinbx) &C. abs? Therefore, et (6:24+2 Sinz+) +C Therefore the required solution of the equation (3) is, 9= $ (C2526+ 2 sinzt) + ce-t (Answer), et

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