Chapter 5.3, Problem 7P

1.

To determine

A lower bound for the radius of convergence of the series of solution for $y^{″}-y=0$ with the initial values $x_0=0$.

2.

To determine

A lower bound for the radius of convergence of the series of solution for $y^{″}+3y^{\prime }=0$ with the initial values $x_0=0$.

3.

To determine

A lower bound for the radius of convergence of the series of solution for $y^{″}-x{y}^{\prime }-y=0$ with the initial values $x_0=0$.

4.

To determine

A lower bound for the radius of convergence of the series of solution for $y^{″}-x{y}^{\prime }-y=0$ with the initial values $x_0=1$.

5.

To determine

A lower bound for the radius of convergence of the series of solution for $y^{″}+k^2{x}^{2}y=0$ with the initial values $x_0=0$.

6.

To determine

A lower bound for the radius of convergence of the series of solution for $\left(1-x\right)y^{″}+y=0$ with the initial value $x_0=0$.

7.

To determine

A lower bound for the radius of convergence of the series of solution for $y^{″}+x{y}^{\prime }+2y=0$ with the initial values $x_0=0$.

8.

To determine

A lower bound for the radius of convergence of the series of solution for $x{y}^{″}+y^{\prime }+xy=0$ with the initial value $x_0=1$.

9.

To determine

A lower bound for the radius of convergence of the series of solution for $\left(3-x^2\right)y^{″}-3x{y}^{\prime }-y=0$ with the initial value $x_0=0$.

10.

To determine

A lower bound for the radius of convergence of the series of solution for $2y^{″}+x{y}^{\prime }+3y=0$ with the initial values $x_0=0$.

11.

To determine

A lower bound for the radius of convergence of the series of solution for $2y^{″}+\left(x+1\right)y^{\prime }+3y=0$ with the initial values $x_0=2$.