## Answers

1242 Solution Given that y= A x ln (x) + Bx + F is the particular solution of the second order and also given that 24"=2 where y'=4 at point (3,2) =) y"= Integrating on both sides » y'= 2 lonxe tc - ③ Again Integrating on both sides =) Y = 2/& lns -&) + Catf >> y = 28 (18-9&+C&+F > y = 28 21 (8)+((-2)x+F comparing with ☺ eq. B: (-2, A=2 ie, y = 2880() + B8+ F At (3,2), y'-dy = 4

(from @ . W.K.T » 1 - - 9 Qn(3)+c >>C= 4-2 ln(3) =) B=(-2 > B: 4-286(3)-2 =) B=2-2 ln (3) -) B= -0.197 (substitute 'e'value) Now, y= 2x ln(2) - 0.1978+F (3,2) lies on the curve 3) 2= 2x3 In (3) - 0.197(3)+ F → 9=6.04F - If=-47 Hence ly=98 ln (&)-0.1978-4 1 Therefore Linear DEQ is variable Sepetable

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