DSolve[y''[t] + y[t] == 1, y[t], t]

\(\(y1[t_] = y[t] /. %
\)\)

Solve[{y1[0] == 0, y1'[0] == 0},  {C[1], C[2]}]

y2[t_] = y1[t] /. %

Plot[y2[t], {t, 0, 5}]

\(Plot[{y1[t] /. {C[1] -> 3, C[2] -> 1}, \ \ 
        y1[t] /. {C[1] -> \(-1\), C[2] -> \(-2\)}, 
	
        y1[t] /. {C[1] -> 1, C[2] -> 0}}, 
	{t, 0, 10}]\)

DSolve[{y''[t] + y[t]  ==  1, y[0] == 0, y'[0] == 0}, 
      y[t], t]

Plot[y[t] /. %, {t, 0, 10}]