Question

9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (r²−6r+13)²r²(r+2)³=0 Write the nine fundamental solutions to the differential equation.

Answer 1

The nine fundamental solutions to the differential equation (r²−6r+13)²r²(r+2)³=0 are (3±2i), 0 (multiplicity 2), and -2 (multiplicity 3).

Step-by-step explanation:

Fundamental solutions to the differential equation:

The characteristic equation factors as follows: (r²−6r+13)²r²(r+2)³=0. To find the fundamental solutions, we set each factor equal to zero and solve for r. The nine fundamental solutions are: r = (3±2i), r = 0 (multiplicity 2), and r = -2 (multiplicity 3).