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PhD Student

Determine the recursive formulas for the Taylor methodof order 2 for the initial value problem$$ y^{\prime}=x y-y^{2}, \quad y(0)=-1 $$

Determine the recursive formulas for the Taylor methodof order 4 for the initial value problem$$ y^{\prime}=x^{2}+y, \quad y(0)=0 $$

$$y^{\prime \prime}+y=0$$

If $$F_{\mathrm{ext}}(t)=0$$, equation (3) becomes

$$m y^{\prime \prime}+b y^{\prime}+k y=0$$

For this equation, verify the following:

(a) If $$y(t)$$ is a solution, so is $$c y(t)$$, for any constant $$C$$.(b) If $$y_{1}(t)$$ and $$y_{2}(t)$$ are solutions,so is their sum $$y_{1}(t)+y_{2}(t)$$.

$$y^{\prime \prime}-10 v^{\prime}+26 y=0$$

$$y^{\prime \prime}-4 y^{\prime}+7 y=0$$