Verify that the functions cos 3x and sin 3x are solutions of the differential equation y" + 9y = 0 on the interval (-∞, 00). Then use the Wronskian to show that they form a fundamental set of solutions. Finally, write the general solution for the differential equation. The function v. = x2 is one solution of the differential equation r2y" – 2ry! 1 2y - O Use

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Chapter2: Second-order Linear Odes
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Verify that the functions cos 3x and sin 3x are solutions of the differential equation y" + 9y = 0 on
the interval (-o, 00). Then use the Wronskian to show that they form a fundamental set of
solutions. Finally, write the general solution for the differential equation.
The function v. = x2 is one solution of the differential eguation r2," – 2ry! 1 2v – 0
IIse
Transcribed Image Text:Verify that the functions cos 3x and sin 3x are solutions of the differential equation y" + 9y = 0 on the interval (-o, 00). Then use the Wronskian to show that they form a fundamental set of solutions. Finally, write the general solution for the differential equation. The function v. = x2 is one solution of the differential eguation r2," – 2ry! 1 2v – 0 IIse
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