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Verify that the given functions y₁(t) = t and y2(t) = te³t satisfy the corresponding homogeneous equation; then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. t²y" − t(3t+ 2)y' + (3t + 2)y = 7t³, t > 0. - NOTE: Use t as the independent variable. 1 ) = c₁t+c₂te³ − (91²4 + 91³ + 6t² + 2t)

Verify that the given functions y₁(t) = t and y2(t) = te³t satisfy the corresponding homogeneous equation; then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. t²y" − t(3t+ 2)y' + (3t + 2)y = 7t³, t > 0. - NOTE: Use t as the independent variable. 1 ) = c₁t+c₂te³ − (91²4 + 91³ + 6t² + 2t)

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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Verify that the given functions y₁(t) = t and y₂(t) = te³t satisfy the corresponding homogeneous equation; then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. t²y" - t(3t+2)y' + (3t+ 2)y = 7t³, t > 0. NOTE: Use t as the independent variable. Y(t)=c₁t+c₂te³t - 1/² (91¹ + 91³ + 6t² +21) 8
Transcribed Image Text:Verify that the given functions y₁(t) = t and y₂(t) = te³t satisfy the corresponding homogeneous equation; then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. t²y" - t(3t+2)y' + (3t+ 2)y = 7t³, t > 0. NOTE: Use t as the independent variable. Y(t)=c₁t+c₂te³t - 1/² (91¹ + 91³ + 6t² +21) 8
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