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(a). Find the general solutions: (al) y' + In(t)y = +-++2 t¯t+2 μ(t) = e√ In(t) dt = ef In(t) dt = etln(t) – td ln(t) e. = etln(t)—t = t¹e¯t. Using the formula, - y(t): tte-t Stedt, Here the integral ft²e¯dt = − √ t² de¯ S t²de¯* −t²e¯† = −t²e¯ + √2te¯dt =-t²et - 2 ftdet = -t²et - 2tet +2 fedt = -1²et - 2tet - 2et + C. The solution is 1 y(t) = (-t²et - 2tet - 2et + C) = t1 (-1² - 2t-2+ Ce²) (−t²

(a). Find the general solutions: (al) y' + In(t)y = +-++2 t¯t+2 μ(t) = e√ In(t) dt = ef In(t) dt = etln(t) – td ln(t) e. = etln(t)—t = t¹e¯t. Using the formula, - y(t): tte-t Stedt, Here the integral ft²e¯dt = − √ t² de¯ S t²de¯* −t²e¯† = −t²e¯ + √2te¯dt =-t²et - 2 ftdet = -t²et - 2tet +2 fedt = -1²et - 2tet - 2et + C. The solution is 1 y(t) = (-t²et - 2tet - 2et + C) = t1 (-1² - 2t-2+ Ce²) (−t²

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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(a). Find the general solutions: (al) y' + In(t)y = +-++2 t¯t+2 μ(t) = e√ In(t) dt = ef In(t) dt = etln(t) – td ln(t) e. = etln(t)—t = t¹e¯t. Using the formula, - y(t): tte-t Stedt, Here the integral ft²e¯dt = − √ t² de¯ S t²de¯* −t²e¯† = −t²e¯ + √2te¯dt =-t²et - 2 ftdet = -t²et - 2tet +2 fedt = -1²et - 2tet - 2et + C. The solution is 1 y(t) = (-t²et - 2tet - 2et + C) = t1 (-1² - 2t-2+ Ce²) (−t²
Transcribed Image Text:(a). Find the general solutions: (al) y' + In(t)y = +-++2 t¯t+2 μ(t) = e√ In(t) dt = ef In(t) dt = etln(t) – td ln(t) e. = etln(t)—t = t¹e¯t. Using the formula, - y(t): tte-t Stedt, Here the integral ft²e¯dt = − √ t² de¯ S t²de¯* −t²e¯† = −t²e¯ + √2te¯dt =-t²et - 2 ftdet = -t²et - 2tet +2 fedt = -1²et - 2tet - 2et + C. The solution is 1 y(t) = (-t²et - 2tet - 2et + C) = t1 (-1² - 2t-2+ Ce²) (−t²
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