$k_1$

$k_2$

$k_3$

$\frac{1}{6\left(1+\lambda \right)}{V}^{\prime }-\frac{\left(7+\lambda \right){\tau }_c^2}{6{\left(1+\lambda \right)}^4}{\left(V^{\prime }\right)}^3$

$-\frac{V^{‴}}{6\left(1+\lambda \right)}$

$\frac{1}{2\left(1+\lambda \right)}{V}^{\prime }$

$k_4$

$k_5$

$\frac{\left(15+\lambda \right){\tau }_c^3}{24{\left(1+\lambda \right)}^5}{\left(V^{\prime }\right)}^4-\frac{1}{24\left(1+\lambda \right)}{V}^{\prime }$

$\frac{V^{‴}}{12}\frac{2\left(3+\lambda \right){\tau }_c}{{\left(1+\lambda \right)}^3}{V}^{\prime }-\frac{1}{1+\lambda }$