1.3 Wronskian

If a(t), b(t) are the solutions to a linear homogeneous ODE, then their wronskian denoted $W(a,b)(t)$ or $W(a,b)$ is $a{b}^{\prime }-a^{\prime }b$

Implications of the Wronskian §

• If the wronskian is not zero, then a, b are linearly independent and are said to form a fundamental set of solutions
• Otherwise they are linearly dependent and are not a fundamental set of solutions