Question: Solve the initial value problem. 2 dy 4x2 - x - 3 X dx (x+ 1)(y+1) , y(1) =3 The solution is (Type an implicit

Solve the initial value problem. 2 dy 4x2 - x - 3 X dx (x+ 1)(y+1) , y(1) =3 The solution is (Type an implicit solution. Type an equation using x and y as the variables.)72dy 42 2 - 3 da CatDIY+1) , 8(1) = 3. [ (4 + 1 ) dy = 1 42 - x - 3 dry - D. Consider partial fractions of R. H.S. A 2 2 (2+ 1 ) + X + 1 42 - 2-3- Ax( 2+1)+ B(a+D)+ c(x2). - 3 = B . 2 = C. 3 = 1 0 = 2A +2 B+C. 0 = 2A + 2 ( - 3) + 2 - 0=20-4 A = 2 Nom from | ( y + 1 ) dy = 1x + (: 3) + 2 ath 3 4 2 2 + y = 2 logx + 3- * + 2 log ( 2 +1) + c . Now y ( 1) = 3 - 32 2 +3 = 2 609 1 + 3 . I+2log ( 1+ ) +C 2 = 2log ( 2) + c . C - 2 - 2log 2 . : solution is 42 2 + y = 2 logx + 3 + 2 log ( 2 + D)+ - - 2log 2

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