Consider the differential equation

$\frac{d^{2}x}{d{t}^2}+3\frac{dx}{dt}+2x=f(x)$

Where $f(x)$ is the input and is a function of the output,

$x.$ If $f(x)=sin(x),$ linearize the differential equation

for small excursions $1)x=0$ and $2)x=.$

Try this yourselves!

a$){}^{}x+3{}^{}x+x=0$

b$){}^{}x+3{}^{}x+3x=0$

c$)3{}^{}x+3{}^{}x+x=0$

d$)3{}^{}x+3{}^{}x+3x=0$