Chapter 4.1, Problem 37E

(A)

To determine

To find: The general solution of the equation $y^{″}=0$ with the help of observations as $D^n{x}^{n-1}=0\text{ and }{D}^n{x}^n=n\text{!}$ and $n=1,2,3,\mathrm{....}n$

(B)

To determine

The general solution of the equation $y^{‴}=0$ with the help of observations as $D^n{x}^{n-1}=0\text{ and }{D}^n{x}^n=n\text{!}$ and $n=1,2,3,\mathrm{....}n$

(C)

To determine

To find: The general solution of the equation $y^4=0$ with the help of observations as $D^n{x}^{n-1}=0\text{ and }{D}^n{x}^n=n\text{!}$ and $n=1,2,3,\mathrm{....}n$.

(d)

To determine

The general solution of the equation $y^{″}=2$ with the help of observations as $D^n{x}^{n-1}=0\text{ and }{D}^n{x}^n=n\text{!}$ and $n=1,2,3,\mathrm{....}n$.

(e)

To determine

The general solution of the equation $y^{‴}=3$ with the help of observations as $D^n{x}^{n-1}=0\text{ and }{D}^n{x}^n=n\text{!}$ and $n=1,2,3,\mathrm{....}n$.

(f)

To determine

The general solution of the equation $y^4=24$ with the help of observations as $D^n{x}^{n-1}=0\text{ and }{D}^n{x}^n=n\text{!}$ and $n=1,2,3,\mathrm{....}n$.