Solution Found!
Suppose that L1 D a1D2 C b1D C c1 and L2 D a2D2 C b2D Cc2,
Chapter , Problem 21(choose chapter or problem)
QUESTION:
Suppose that \(L_{1}=a_{1} D^{2}+b_{1} D+c_{1}\) and \(L_{2}=a_{2} D^{2}+b_{2} D+c_{2}\), where the coefficients are all constants, and that x(t) is a four times differentiable function. Verify that \(L_{1} L_{2} x=L_{2} L_{1} x\).
Questions & Answers
QUESTION:
Suppose that \(L_{1}=a_{1} D^{2}+b_{1} D+c_{1}\) and \(L_{2}=a_{2} D^{2}+b_{2} D+c_{2}\), where the coefficients are all constants, and that x(t) is a four times differentiable function. Verify that \(L_{1} L_{2} x=L_{2} L_{1} x\).
ANSWER:Step 1 of 3
It is mentioned that x(t) is a four time differential function thus,
\(D^{4} x(t)=x^{\prime \prime \prime \prime}=k\)