y(t)

f(t,y) = $\displaystyle {\left(t^{2} + 1\right)} y\left(t\right)$

1st derivative of f(t,y) wrt time = $\displaystyle {\left(t^{4} + 2 \, t^{2} + 2 \, t + 1\right)} y\left(t\right)$

2nd derivative of f(t,y) wrt time = $\displaystyle {\left(t^{6} + 3 \, t^{4} + 6 \, t^{3} + 3 \, t^{2} + 6 \, t + 3\right)} y\left(t\right)$

3rd derivative of f(t,y) = $\displaystyle {\left(t^{8} + 4 \, t^{6} + 12 \, t^{5} + 6 \, t^{4} + 24 \, t^{3} + 24 \, t^{2} + 12 \, t + 9\right)} y\left(t\right)$