(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
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
Related questions
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can you explain step by step
![(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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeefd442-7c64-4a51-8ed1-c0196ac6a13e%2F6aa41264-3700-4a37-9145-ef5836e6ddf2%2Fnd1qmyp_processed.png&w=3840&q=75)
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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