Consider the differential equation y" - y' – 12y = 0. Verify that the functions e3x e4x form a fundamental set of solutions of the differential equation on the interval (-o, 0). and The functions satisfy the differential equation and are linearly independent since the Wronskian -3x 4x + 0 for -o < x < 0. Form the general solution. y =

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Chapter2: Second-order Linear Odes
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Consider the differential equation
у" - у' — 12у %3D 0.
Verify that the functions e
-3x
and e
4x
form a fundamental set of solutions of the differential equation on the interval (-0, ∞).
The functions satisfy the differential equation and are linearly independent since the Wronskian We
-3x
+ 0 for -0 < x < ∞.
=
Form the general solution.
y =
Transcribed Image Text:Consider the differential equation у" - у' — 12у %3D 0. Verify that the functions e -3x and e 4x form a fundamental set of solutions of the differential equation on the interval (-0, ∞). The functions satisfy the differential equation and are linearly independent since the Wronskian We -3x + 0 for -0 < x < ∞. = Form the general solution. y =
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