Determine if the following differential equation is exact. If it is, (1) find its general solution...

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Determine if the following differential equation is exact. If it is, (1) find its general solution in explicit form. + 5x)dr + (In() – 8)dy = 0, x > 0. (2) Find the general solution of the following differential equations. (a) y" - 2y'-2y D0 %3D (b) 9y/"+6y+y 0 (c) y"-2y'+2y = 0 (3) Solve the initial value problem 9y" – 12y + 4y = 0; y(0) = 2, y(0) = -1 %3D %3D (4) Find a particular solution of the differential equation y" + 2y/ + 5y = 3 sin(2t) (5) Find the general solution of the differential equation y" + 3y' + 2y = 2e-2t Determine if the following differential equation is exact. If it is, (1) find its general solution in explicit form. + 5x)dr + (In() – 8)dy = 0, x > 0. (2) Find the general solution of the following differential equations. (a) y" - 2y'-2y D0 %3D (b) 9y/"+6y+y 0 (c) y"-2y'+2y = 0 (3) Solve the initial value problem 9y" – 12y + 4y = 0; y(0) = 2, y(0) = -1 %3D %3D (4) Find a particular solution of the differential equation y" + 2y/ + 5y = 3 sin(2t) (5) Find the general solution of the differential equation y" + 3y' + 2y = 2e-2t