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+ 2 y' + 5y = 8x e cos(5x) %3D d the Solutions to its Characteristic Equation raracteristic Solutions: R = - 1+ 2i etermine the General Solution for the Particular Side of the Differential Equation. A yp = [Ax + B]e cos( 5x) + [Cx + D]e* sin(5x) B y, = [Ax? + Bx]e *i cos(5x) + [Ax² + Bx]e* sin(5x) yp = [Ax³ + Bx2 + Cx + D]e* cos(5x) D y, = -Ax e cos(5x) + 2Bx et* sin(5x) E y, = [Ax? + Bx]e* cos(5x) + [Cx? + Dx]e* sin(5x) F y, [Ax + B]e cos(5x) + [Ax + B]e sin(5x)

+ 2 y' + 5y = 8x e cos(5x) %3D d the Solutions to its Characteristic Equation raracteristic Solutions: R = - 1+ 2i etermine the General Solution for the Particular Side of the Differential Equation. A yp = [Ax + B]e cos( 5x) + [Cx + D]e* sin(5x) B y, = [Ax? + Bx]e *i cos(5x) + [Ax² + Bx]e* sin(5x) yp = [Ax³ + Bx2 + Cx + D]e* cos(5x) D y, = -Ax e cos(5x) + 2Bx et* sin(5x) E y, = [Ax? + Bx]e* cos(5x) + [Cx? + Dx]e* sin(5x) F y, [Ax + B]e cos(5x) + [Ax + B]e sin(5x)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 1CR
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Given the differential equation y" + 2 y' + 5y = 8x e cos(5x) And the Solutions to its Characteristic Equation Characteristic Solutions: R = -1 + 2i Determine the General Solution for the Particular Side of the Differential Equation. A y, = [Ax + B]e cos(5x) + [Cx + D]e sin(5x e4x B y, = [Ax? + Bx]e cos(5x) + [Ax2 + Bx]e sin(5x) %3D y, = [Ax³ + Bx² + Cx + D]e cos(5x) y, = - Ax e cos(5x) + 2Bx e sin(5x) E y, = [Ax? + Bx] e* cos( 5x) + [Cx? + Dx]e sin(5x) (F y, = [Ax + B]e* cos(5x) + [Ax + B]e* sin(5x)
Transcribed Image Text:Given the differential equation y" + 2 y' + 5y = 8x e cos(5x) And the Solutions to its Characteristic Equation Characteristic Solutions: R = -1 + 2i Determine the General Solution for the Particular Side of the Differential Equation. A y, = [Ax + B]e cos(5x) + [Cx + D]e sin(5x e4x B y, = [Ax? + Bx]e cos(5x) + [Ax2 + Bx]e sin(5x) %3D y, = [Ax³ + Bx² + Cx + D]e cos(5x) y, = - Ax e cos(5x) + 2Bx e sin(5x) E y, = [Ax? + Bx] e* cos( 5x) + [Cx? + Dx]e sin(5x) (F y, = [Ax + B]e* cos(5x) + [Ax + B]e* sin(5x)
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