DSolve[x'[t] == t^3 - t, x[t], t]

DSolve[e^x[t] x'[t] == t + 1, x[t], t]

DSolve[x'[t] + a x[t] + b c^t x[t] == 0, x[t], 
      t]

DSolve[x'[t] - 3  x[t] == 5, x[t], t]

DSolve[{x'[t] - 3  x[t] == 5, x[0] == 1}, x[t], 
      t]

DSolve[3  x'[t] + 2  x[t] + 16 == 0, x[t], t]

DSolve[{3  x'[t] + 2  x[t] + 16 == 0, x[0] == 1}, x[t], 
      t]

DSolve[x'[t] + 2  x[t] == t^2, x[t], t]

DSolve[{x'[t] + 2  x[t] == t^2, x[0] == 1}, x[t], 
      t]

Plot[x^3 + x^2 - x - 1, {x, -2, 2}]

Plot[3  x^2 + 1, {x, -10, 10}]

Plot[x*E^x, {x, -5, 2}]