Question

none of the above specify Problem 4 Solve the initial value problem (2x - xy + xyl)dx - ( ) dy- 01) -- and then provide the provide the numerical value of FIVE A student Rounded of the final answer towers Founded or the final answer to f e e d that there was follow (10 points) fyour numerical answer for the limit must be written here) *. You must provide some intermediate results obtained by you while solving the problem above 1) The impli he implicit solution of the initial value problem is described by the equation as follows (marka correct variant) (5 points): 3 xy - (x + 1) y?+ 9x20 x? + y - 4x+y +(2+x+/2)y? - 17 = 0; x2 + y - 4x+y+(1+ ) y? - 33 = 0 x -xy+ (2x-10) +12 = 0. 2x - 3xy-(1 + x?)y? + 19 = 0 rẻ -xy+(2x-10) y = 0 none of the above, specify: 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) (5 points): y=-1-400-80x4172-83 4-5+x) 4-5+1) IIIIIIII x +41r.-8x 41-5+2) X- 480-96x+41-Br 40-5+x) -1 + 4x2 +137 + 18 x2 +14* 4+ 2 -1 + 4x2 - 137+18 r2 + 14x ol 3r? +7V19+8r2+r 2+ 2 -3x-76+93x2 +884 2(1+x2)

Answer 1

. (24-bry + xy) dhe+ (1-42²+64 +2²2yIdy zo Comparing in with Mde+Ndy zo M= {u-8 ny try N=1-44²+44 +wy My = -8x + 2xy Ny = - 8 ut any My = Nu ie, (i) is an exact Difterential equation. ..General solution of (1) is rdu+ Sitarm free of in Nidy=c ما

Slan-Bxy tay?) chat Serruysdy=c pot - B9 ( 9 + 994) +9+4422 vez_4de?y + xy + y +248=C. 2²402-114 + ( 22 + 2) ye_c x2 (42+04+ (22+2)y=c. 2 41)=-2 1-(4-1) (-2) + (²+2) (4)=C 1+6 +5 (4)=C 146+10=0 [c=11 . x² (42=114+ (2 + 2) y² = 17 cor) 1x79-42²y +(2+ 2 ² 2 ² 1120. option is. meleon

(24 )y+ (1–422)+(x2-17) =0. PS a quadratic equation in y = -b I J 6²_400 20 = -(1-4x2) (-4re2-)2-4 (2+243)(1217) 2/2 + 2 2 2 2-4+4x2+ ) 141624_8x2= 414 +224) (3:17) = + + 4x + + 16x4_8x² - 2 (4x²+x4_68-1783) (4+x2) = 4+4+*+1+1624_8x2882-224+ 136 +3433 (4+x2) =x+42²7 / 137+14x4 + 18x² (4+²) ie option (5,6. .