# Find y: $$\displaystyle{y}{''}-{9}{y}'+{14}{y}={0}$$

Find y:
$y{}^{″}-9{y}^{\prime }+14y=0$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

yaum3xg1
Given,
$y-9{y}^{\prime }+14y=0$
This is a second order linear ordinary differential equation.
$\left({D}^{2}-9D+14\right)y=0$
Auxiliary equation:
${m}^{2}-9m+14=0$
$\left(m-7\right)\left(m-2\right)=0$
$m=2$ or $m=7$
Thus
$y={c}_{1}{r}^{2x}+{c}_{2}{e}^{7x}$