Ctice for lest $1$

Part Iol $3$

Determine the recursive formulas for the Taylor method of order $4$ for the initial value problem below. Note whether or not $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}$ is bounded.

$y=x^2+y,y(0)=0$

Let $y^{\text{'}}=f(x,y).$ Find $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}$ and determine whether or not it is bounded. Select the correct choice below and fill in the answer box to complete your choice.

A$.\frac{\text{d}\text{e}\text{l}\text{t}}{\text{d}\text{e}\text{l}\text{y}}(xy)=$ is not bounded

$$

B$.\frac{dt}{dy}(x,y)=$ is bounded.