Pregunta: Find y as a function of x if y′′′−5y′′−y′+5y=0 y(0)=−1, y′(0)=−1, y′′(0)=−97.

The given differential equation is, $\mathrm{y}{}^{‴}-5\mathrm{y}{}^{″}-{\mathrm{y}}^{\prime }+5\mathrm{y}=0\dots \left(1\right)$

Let $\mathrm{y}={\mathrm{e}}^{\mathrm{m}\mathrm{x}}$ be a trial solution of (1)

Then the auxiliary equation of (1...