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Use Variation of Parameters to find the general solution of the equation Py" (t) – 4ty (t) + 6y(t) = t³ + 1, t>0 The Variation of Parameters guarantees a particular solution in the form Yp(t) = y1 (t)v1 (t) + y2(t)v>(t). Hint: The functions y1 (t) = t° and y2(t) = t³ are linearly independent solutions of the homogeneous solution for t > 0. (a) The Wronskian of y1(t) and y2(t) is W (y1, 42)(t) : (b) Find the function v1(t) vi(t) =

Use Variation of Parameters to find the general solution of the equation Py" (t) – 4ty (t) + 6y(t) = t³ + 1, t>0 The Variation of Parameters guarantees a particular solution in the form Yp(t) = y1 (t)v1 (t) + y2(t)v>(t). Hint: The functions y1 (t) = t° and y2(t) = t³ are linearly independent solutions of the homogeneous solution for t > 0. (a) The Wronskian of y1(t) and y2(t) is W (y1, 42)(t) : (b) Find the function v1(t) vi(t) =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 32E
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Use Variation of Parameters to find the general solution of the equation Py" (t) – 4ty (t) + 6y(t) = t³ + 1, t>0 The Variation of Parameters guarantees a particular solution in the form Yp(t) = y1 (t)v1 (t) + Y2(t)v>(t). Hint: The functions y1 (t) = t° and y2(t) = t³ are linearly independent solutions of the homogeneous solution for t > 0. (a) The Wronskian of y1(t) and y2(t) is W (y1, 42)(t) · %3D (b) Find the function v1(t) v1(t) =
Transcribed Image Text:Use Variation of Parameters to find the general solution of the equation Py" (t) – 4ty (t) + 6y(t) = t³ + 1, t>0 The Variation of Parameters guarantees a particular solution in the form Yp(t) = y1 (t)v1 (t) + Y2(t)v>(t). Hint: The functions y1 (t) = t° and y2(t) = t³ are linearly independent solutions of the homogeneous solution for t > 0. (a) The Wronskian of y1(t) and y2(t) is W (y1, 42)(t) · %3D (b) Find the function v1(t) v1(t) =
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