Linear equations of second order with constant coefficients. Find all solutions on (−∞,+∞). y−4y=0

Chaya Galloway

Answered question

2021-05-27

Linear equations of second order with constant coefficients. Find all solutions on
$(-\infty ,+\infty )$. y−4y=0

Answer & Explanation

Willie

Skilled2021-05-28Added 95 answers

The characteristic equation is given by $\left({r}^{2}\right)-4=0$ and has the roots ${r}_{1}=2\text{and}{r}_{2}=-2$. The general solution is given by $y={c}_{1}{e}^{2}x+{c}_{2}{e}^{-2}x$ where e1 and e2 are arbitrary costant.