Exercise · ZW-WRONSKIAN-008 · ★★☆ Intermediate
Let \(y_1,y_2\) be solutions of \(y''+py'+qy=0\), with \(p,q\) continuous, and suppose \(W(y_1,y_2)(t_0)\neq0\) at a point \(t_0\). What follows?
Choose one option.
Show answer
- A. They form a fundamental set: \(c_1y_1+c_2y_2\) gives every solution
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Explanation
A nonzero Wronskian at a single point suffices: it lets you match any \(y(t_0)\) and \(y'(t_0)\), and by uniqueness you get every solution.
More practice problems: wronskian
- ZW-WRONSKIAN-001 Compute the Wronskian W(e^2t,e^3t).
- ZW-WRONSKIAN-002 Compute W(t,t^2).
- ZW-WRONSKIAN-003 Compute W(cos t,sin t).
- ZW-WRONSKIAN-004 Compute W(e^t,2e^t) and interpret the result.
- ZW-WRONSKIAN-005 Compute W(e^-t,te^-t).
- ZW-WRONSKIAN-006 Compute W(sin 2t,cos 2t).
- ZW-WRONSKIAN-007 For t>0, compute W(t, tln t).
- ZW-WRONSKIAN-009 Let y_1,y_2 be solutions of y''+py'+qy=0 with p,q continuous, and W(y_1,y_2)(t_0)=0 at some t_0. Wh…