Chapter 2.3, Problem 50E

(a)

To determine

Explain the existence and uniqueness of a solution of IVP consisting of $x{y}^{\prime }-4y=x^6{e}^x$ for the given initial condition $y\left(0\right)=0$.

(b)

To determine

Explain the existence and uniqueness of a solution of IVP consisting of $x{y}^{\prime }-4y=x^6{e}^x$ for the given initial condition $y\left(0\right)=y_0,y_0>0$.

(c)

To determine

Explain the existence and uniqueness of a solution of IVP consisting of $x{y}^{\prime }-4y=x^6{e}^x$ for the given initial condition $y\left(x_0\right)=y_0,y_0>0$.