Chapter 3.1, Problem 29P

Program Plan Intro

Program Description: Purpose of problem is to verify that $y_1$ and $y_2$ are solutions of the differential equation $x^2{y}^{″}-4x{y}^{\prime }+6y=0$, both satisfying the initial conditions $y\left(0\right)=0\text{ and }{y}^{\prime }\left(0\right)=0$ and also explain that these facts do not contradict Theorem 2.

Summary introduction: Problem will use if the functions $p,q,\text{ and }f$ are continuous on the open interval I containing the point a .

The equation $y^{″}+p\left(x\right)y^{\prime }+q\left(x\right)y=f\left(x\right)$ has unique solution on the entire interval I that satisfy the initial condition $y\left(a\right)=b_0\text{ and }{y}^{\prime }\left(a\right)=b_1$ .