2.1.7.4 ✓ Maple. Time used: 0.004 (sec). Leaf size: 5

ode:=diff(x(t),t) = x(t)^2-3*x(t)+2; 
ic:=[x(0) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\begin{align*} x = 1 \end{align*}

Maple trace

Methods for first order ODEs: 
--- Trying classification methods --- 
trying a quadrature 
trying 1st order linear 
trying Bernoulli 
trying separable 
<- separable successful