Question: please help me MATH DIFFERENTIAL AND INTEGRATION. thanks. A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows.

please help me MATH DIFFERENTIAL AND INTEGRATION. thanks.

A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. ( r2 - 4r + 8)' Kr+ 3)2 = 0 Write the nine fundamental solutions to the differential equation. y1= )2 = e^(-3t) )3 = te^(-3t) y4 = th2ent ys = e^(-3t) cos(-3t) y6 = e^(-3t) tsin(-3t) = e^(-3t) tcos(-3t) y8 = e^(-3t)t^(2)sin(- yo = e^(-3t)t^(2)cos(; (You can enter your answers in any order.)Show all your work! [10p] Question 1. Solve the following separable ode: dy - cey = 5ey, y(0) = 3. dx\f[10p] Question 3. Consider the equation: (x ty) 2 da + (2xy + x2 -1)dy =0. a Check if it is exact or not. b) If exact, solve it. If not exact, transform into an exact one

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