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Given that
2t2 y′′ + ty′ - 3 y = 0
Show that this given solution are form a fundamental set of solutions for the differential equation?
Solution
The two solutions from that illustration are
y1(t) = t-1 y2(t) = t3/2
Let's calculate the Wronskian of these two solutions.
Therefore, the Wronskian will never be zero. Memorizes that we can't plug t = 0 in the Wronskian. It would be a problem in determining the constants in the general solution, except that we as well can't plug t = 0 in the solution either and thus this isn't the problem which it might appear to be.
So, as the Wronskian isn't zero for any t the two solutions form a fundamental set of solutions and the general solution is as
y(t) = c1t-1+ c2 t3/2as we claimed in that illustration.
To this point we're determined a set of solutions then we've claimed which they are actually a fundamental set of solutions. Certainly, you can now verify all those claims which we've made, though this does bring up a question.
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