determine whether the given differential equation is exact. If it is exact, solve it. (please solve both  9)  (x- y^3 +y^2 sin x) dx = (3xy^2 + 2y cos x) dy 11) (y ln y-e^-xy)dx+(1/y+xlny)dy=0

Exercises Find the solution of the following Differential Equations 1) y" + y = 3x² 3) "+2y+3y=27x 5) y"+y=6sin(x) 7) y"+4y+4y = 18 cosh(x) 9) (4)-5y"+4y = 10 cos(x) 11) y"+y=x²+x 13) y"-2y+y=e* 15) y+2y"-y'-2y=1-4x³ 2) y"+2y' + y = x² 4) "+y=-30 sin(4x) 6) y"+4y+3y=sin(x)+2 cos(x) 8) y"-2y+2y= 2e* cos(x) 10) y+y-2y=3e* 12) y"-y=e* 14) y"+y+y=x+4x³ +12x² 16) y"-2y+2y=2e* cos(x)

Solve the system of linear equations. x+y+z = -6 x-6y-7z = -29 -7y-5z = 4 O (-8, -7,9) O (-6, -7, 10) O (-7,-8, 9) O (-7,-6, 10) O (9,-7,-8)

4. Solve the following differential equations: a- y" +zy' ty = x² b- y" -4y = Sinx <- 4"+zy! +y=ex ANS- 9- y = ex (4 x + c₂) +x²-4x+6 2X -2X b- y = Ge²x² + cze²x - is sinx -X C- y=Qe + cake + -X