3. Let y" +2y' - 3y = f(x). Find the solution in the cases (a) f(x)=0;...

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3. Let y +2y - 3y = f(x). Find the solution in the cases (a) f(x)=0; (b) f(x) 6x; (c) f(x) = 4 , y(0)-0, y(0) - 1.

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Answer 1

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Given y+24-3y = f(n) fon=0 - 41+2y— 34 = 0 correspondling Auxillary Eguachon is D+2) - 3.30 Dal and D=-3_ Solleision of a f(x) = 402 y+ 2y- y = 4 6 % complementory solunon Y CW) = 1, elt ez e34 Particular Integral is (40) -Yo II B+2D-3 d(0)=B²+

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