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Find the general solution of the differential equation y" - 2y + y = 13et 1+ t² NOTE: Use C₁ and C₂ as arbitrary constants. y(t): =

Find the general solution of the differential equation y" - 2y + y = 13et 1+ t² NOTE: Use C₁ and C₂ as arbitrary constants. y(t): =

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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Find the general solution of the differential equation 13et y" - 2y + y = 1+ t² NOTE: Use C₁ and C₂ as arbitrary constants. y(t) = eTextbook and Media Hint Assistance Used If the functions p, q, and g are continuous on an open interval I and if the functions y, and y, are a fundamental set of solutions of the homogeneous equation y" +p(ty + q(t)y = 0 corresponding to the nonhomogeneous equation y" +p(ty' + g(t)y = g(t), then Y₂ (5)g(s) a particular solution of the nonhomogeneous equation is y(t) = -3₁(0)1 to W (V1 V₂) (s) conveniently chosen point in I. The general solution is y = c₁v₁(t) + c₂₂(t) + X(t). f as +3₂(1) ds 1₁ (5) 8 (5) ds, where to is any to W (V1.J2) (s)
Transcribed Image Text:Find the general solution of the differential equation 13et y" - 2y + y = 1+ t² NOTE: Use C₁ and C₂ as arbitrary constants. y(t) = eTextbook and Media Hint Assistance Used If the functions p, q, and g are continuous on an open interval I and if the functions y, and y, are a fundamental set of solutions of the homogeneous equation y" +p(ty + q(t)y = 0 corresponding to the nonhomogeneous equation y" +p(ty' + g(t)y = g(t), then Y₂ (5)g(s) a particular solution of the nonhomogeneous equation is y(t) = -3₁(0)1 to W (V1 V₂) (s) conveniently chosen point in I. The general solution is y = c₁v₁(t) + c₂₂(t) + X(t). f as +3₂(1) ds 1₁ (5) 8 (5) ds, where to is any to W (V1.J2) (s)
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