📂Odinary Differential Equations

Solutions to the Homogeneous Second-Order Linear Differential Equation and the Wronskian

Definition[^1]

$$ay^{\prime \prime}+ by^\prime +cy=0$$

Let’s consider the second-order linear homogeneous differential equation given above. Let’s call $W$ the Wronskian. If $W (y_{1}, y_{2}) \ne 0$, then we call $\left\{ y_{1}, y_{2} \right\}$ the fundamental set of solution for the given differential equation.