Problem #3 (20 points) Solve the initial value problem (2 x - 6xy + xy') dx + (1 - 3x2 + (2 + x7) >) dy = 0, v(1) = -4 and then provide the numerical value of lim y(x) rounded-off to FIVE *+ +60 significant figures. A student rounded-off the final answer to FIVE significant figures and found that the result was as follows (10 points): (your numerical answer for the limit must be written here) Also, you must provide some intermediate results obtained by you while solving the problem above: 1) The implicit solution of the initial value problem is described by the equation as follows (mark a correct variant) (6 points): 3xy - (x)+1)>+9x =0 x' +xy+ (2x+ 10) y? - 10 = 0; x- xy+(2x - 10) y? + 12 = 0 2x2 -3xy - (1+ x )y + 19 = 0 x2 - xy + (2x - 10) yz = 0 x2 + y - 3x y + (1+5 ) y2 - 33 = 0 2) The explicit solution for the value of y as the function of x is described by the explicit formula as follows (mark a correct variant) (4 points): -1+312-/7,19+Bri+ri 2+r (400-80x+41r-ar 1(-5+x) -x-,/41x-8r 4(-5+x) *+41r-8r 4(-5+x) X- 480-96x+41x2-8x 4(-5+x) -1+3x*+/7,/19+Bra+x V= 2+r -3x-76+93.x2+8.r 2(1+r) 3x-4+49r/+3610 Y= 2(1+r)