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Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" + 8y' + 25y = 7te-4t cos 3t - -3te-3t cos 4t

Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" + 8y' + 25y = 7te-4t cos 3t - -3te-3t cos 4t

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" + 8y' + 25y = 7te¹ cos 3t - 3te-³t cos 4t -4t ○ Y(t) = t(Aot + A₁)e¯ cos 3t + t (Cot + C₁)e-³¹ sin 4t. ○ Y(t) = (Aot + A₁)e4¹ cos 3t + (Cot + C₁)e-³t sin 4t. (Aot + A₁)e-4¹ cos 3t + OY(t) = (Bot + B₁) sin 3t + (Côt + C₁)e-³t cos 4t + (Dût + D₁ )sin 4t. -4t ○ Y(t) = t(Aot + A₁)e-4¹ cos 3t + (Bot + B₁ )e−4¹ sin 3t + t(Cot + C₁)e-³t cos 4t + (Dot + D₁)e−³¹ sin 4t. ○ Y(t) = t (Aot + A₁)e-4t cos 3t + t (Bot + B₁ )e4¹ sin 3t + (Cot + C₁)e-³t cos 4t + (Dot + D₁)e−³¹ sin 4t. -4t
Transcribed Image Text:Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" + 8y' + 25y = 7te¹ cos 3t - 3te-³t cos 4t -4t ○ Y(t) = t(Aot + A₁)e¯ cos 3t + t (Cot + C₁)e-³¹ sin 4t. ○ Y(t) = (Aot + A₁)e4¹ cos 3t + (Cot + C₁)e-³t sin 4t. (Aot + A₁)e-4¹ cos 3t + OY(t) = (Bot + B₁) sin 3t + (Côt + C₁)e-³t cos 4t + (Dût + D₁ )sin 4t. -4t ○ Y(t) = t(Aot + A₁)e-4¹ cos 3t + (Bot + B₁ )e−4¹ sin 3t + t(Cot + C₁)e-³t cos 4t + (Dot + D₁)e−³¹ sin 4t. ○ Y(t) = t (Aot + A₁)e-4t cos 3t + t (Bot + B₁ )e4¹ sin 3t + (Cot + C₁)e-³t cos 4t + (Dot + D₁)e−³¹ sin 4t. -4t
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