Question

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

Linear equations and graphs
Linear equations of second order with constant coefficients. Find all solutions on $$\displaystyle{\left(−∞,+∞\right)}$$. y''−4y=0
The characteristic equation is given by $$\displaystyle{\left({r}^{{2}}\right)}-{4}={0}$$ and has the roots $$r_1=2 \text{ and } r_2=-2$$. The general solution is given by
$$\displaystyle{y}={c}_{1}{e}^{{2}}{x}+{c}_{2}{e}^{{-{{2}}}}{x}$$ where e1 and e2 are arbitrary costant.