You have
$$\dot x = \frac{d}{dt}x = 3x$$
multiply $dt$
$$dx = 3xdt$$
divide $x$
$$\frac{1}{x}dx = 3dt$$
integrate
$$\int \frac{1}{x}dx = \int 3dt$$
$$\ln x + C_{apples} = 3t + C_{oranges}$$
make a fruit salad
$$\ln x = 3t + C_{\text{fruit salad}}$$
exponentializify1
$$x = e^{3t + C_{\text{fruit salad}}}=e^{3t}e^{C_{\text{fruit salad}}}$$
add some chopped chocolate to the salad
$$x = e^{3t}e^{C_{\text{fruit salad}}}=e^{3t}C_{\text{fruit salad with chocolate}}$$
try the salad with $x(0)=\frac32$
$$\frac32 =e^{3\cdot 0}C_{\text{fruit salad with chocolate}}=C_{\text{fruit salad with chocolate}}$$
if you think the salad is appropriately seasoned, serve on 2
$$x(2)=e^{3\cdot 2}C_{\text{fruit salad with chocolate}} = e^6\frac32$$
1that is a word