Question

1. Check whether each function is a solution to the equation given with it. If it is not find an actual solution (a) y' = y2 +1. y(x) =tan(x + C) (b) x'=xt, x= 2. (a) Find a general solution to the equation y" = 3x +2. (b) Find a particular solution such that y(1) = 5 and y'(1) -2,

awnser and explain asap please

Answer 1

son? 0 a) y'= y*+1 is an arbitrary constant) 7 b) E & tant y = atc (where ya dan (x+c)] g'a xt da = dra = stdt lniak + @ Inc . In e-sene ce a ln () = 2 ? 7 F T Ta estos os (alt)=ce ] where câs an astihoy conoscout P 2) a) y = 3x+2 a Integrate with respect tox there y'= 3x² + 2x +4 -0. again ito integrate with respect to a there R = 23 tahtaxtla (Where c, and cq are - to, general isolution is arbitrary constants ) YOx)= a3 + x++42+421 b) 4WUzs , 4412-2 yll) = 3 + + 4+ ( = 5. of P+1+cileas est69 = 5-1-12 = 4-4. ait ce = 72 -

and y' (1) = -2 .. y' () = 3x12 +28(1) +21=-2 : (from 2) +2 +62 = -2.9 5. 2-4-36 - - put (2=-11 in ② then Cl = 76. - (q 24+2 18 - 9 WY Hence, particular isol" is. ya) atas +22 +92-1) the