Chapter 5.3, Problem 9P

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 $y^{″}-x{y}^{\prime }-y=0$ 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 $x_0=1$.

4.

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 $x_0=0$.

5.

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 $x_0=0$.

6.

To determine

A lower bound for the radius of convergence of the series of solution for $\left(2+x^2\right)y^{″}-x{y}^{\prime }+4y=0$ 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 $x{y}^{″}+y^{\prime }+y=0$ with the initial value $x_0=1$.

9.

To determine

A lower bound for the radius of convergence of the series of solution for $\left(1+x^2\right)y^{″}-4x{y}^{\prime }+6y=0$ with the initial value $x_0=0$.

10.

To determine

A lower bound for the radius of convergence of the series of solution for $\left(4-x^2\right)y^{″}+2y=0$ with the initial value $x_0=0$.

11.

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 $x_0=0$.

12.

To determine

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

13.

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 $x_0=0$.

14.

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 $x_0=2$.