Step 5: Set each factor equal to zero to find the roots: r - 2 = 0 gives r = 2, and r - 3 = 0 gives r = 3.
Step 6: Since we have two distinct real roots (2 and 3), the general solution of the differential equation is: y = C1 e^(2x) + C2 e^(3x), where C1 and C2 are constants.
Homogeneous Linear Differential Equations – The question tests the ability to solve a second-order linear homogeneous differential equation with constant coefficients.
Characteristic Equation – It assesses the understanding of deriving the characteristic equation from the differential equation and finding its roots.
General Solution – The question evaluates the ability to write the general solution based on the roots of the characteristic equation.
