To get a feel for higher order ODEs, show that the given functions are solutions and form a basis on any interval. Use Wronskians. In Prob. 6, x > 0,
e^-4x, xe^-4x, x²e^-4x, y"' + 12y" + 48y' + 64y = 0

Question

To get a feel for higher order ODEs, show that the given functions are solutions and form a basis on any interval. Use Wronskians. In Prob. 6, x > 0,

e^-4x, xe^-4x, x²e^-4x, y"' + 12y" + 48y' + 64y = 0

Accepted Answer

From the general solution  y   A x    B x e-4x for x   0  we have y     12y    48   ...

To get a feel for higher order ODEs, show that the given