If y''(t)+p(t)y=0 is nonoscillatory then y''(t)+p(t)y=f(t) is nonoscillatory. p(t) =>0 and f(t)=>0 and f(t) continuous function.

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- May 30th 2010, 12:26 PMmathemanyakoscillation behaviour
If y''(t)+p(t)y=0 is nonoscillatory then y''(t)+p(t)y=f(t) is nonoscillatory. p(t) =>0 and f(t)=>0 and f(t) continuous function.

- Dec 27th 2010, 02:13 PMRebesques
You need just show that if the non-homogeneous problem has oscillatory solutions, then the homogeneous problem has oscillatory solutions.

Now, if y solves the non-homogeneous problem and w solves the homogeneous one, then y-w solves the non-homogeneous problem.