Class 09/08/2021

Suppose the solution to the IVB $\frac{d y}{d x} = f (y), y (0) = 2$ is $y (x) = \frac{2}{1 - x}$ . Let $\overset{y}{ˉ} (x)$ represent the solution to the IVB $\frac{d y}{d x} = f (y), y (1) = 2$ . Find the value of $\overset{y}{ˉ} (0)$ . $\overset{y}{ˉ} (x) = y (x - 1) = \frac{2}{2 - x}$

$\overset{y}{ˉ} (0) = \frac{2}{2 - 0} = 2$

Introduction to First Order Linear Systems

Consider systems of n first order linear differential equations

\frac{d}{d x} ⎣ ⎡ y 1 ⋮ y n ⎦ ⎤ = ⎣ ⎡ P 11 \dots \dots \dots ⋱ \dots P 1 n \dots P nn ⎦ ⎤ x + ⎣ ⎡ g 1 (x) ⋮ g n (x) ⎦ ⎤

Number of columns in the left matrix must be equal to the number of rows in the second matrix.