2.1.1.5 ✓ Mathematica. Time used: 0.003 (sec). Leaf size: 15

ode=D[x[t],t]==3*t^2+4*t; 
ic={x[1]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to t^3+2 t^2-3 \end{align*}