Use Euler’s method to estimate y (1.2), the solution to the IVP (initial value problem)
y' = 2t - y, y (1) = -1, and step size h = 0.1.
Where is the trouble?
The approximate solution to the initial value problem
$\displaystyle \frac{dy}{dt} = f(t, y)$ where $\displaystyle y(t_0) = y_0$
is given by $\displaystyle y_{n+1} = y_n + h f(t_n, y_n)$.
Therefore in your question:
$\displaystyle y(1.1) = y_1 = y_0 + h (2 t_0 - y_0) = -1 + (0.1) (2 - -1) = -1 + 0.3 = -0.7$.
$\displaystyle y(1.2) = y_2 = y_1 + h (2 t_1 - y_1) = -0.7 + (0.1) (2.2 - -0.7) = -0.7 + 0.29 = -0.41$.