Use variation of parameters to find a general solution to the differential equation given that the functions y₁ and y2 are linearly independent solutions to the corresponding homogeneous equation for t> 0. ty' + (6t-1)y' - 6y=7t² e 6t 1 Y₁ = 6t-1, Y₂ = e-6t COL A general solution is y(t) = c₁ (6t-1) + C₂ e - 6t 7 216 (181²-1)

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Chapter2: Second-order Linear Odes
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Differential equations- Help with the question because both answers are incorrect please thank you
Use variation of parameters to find a general solution to the differential equation given that the functions y₁ and y₂ are linearly independent solutions to the
corresponding homogeneous equation for t> 0.
ty' + (6t-1)y' -6y=7t² e-6t.
Y₁ 6t-1,
- 6t
Y₂ = e
A general solution is y(t) = c₁ (6t-1) + C₂ e
- 6t
216 (18t²-1)
Transcribed Image Text:Use variation of parameters to find a general solution to the differential equation given that the functions y₁ and y₂ are linearly independent solutions to the corresponding homogeneous equation for t> 0. ty' + (6t-1)y' -6y=7t² e-6t. Y₁ 6t-1, - 6t Y₂ = e A general solution is y(t) = c₁ (6t-1) + C₂ e - 6t 216 (18t²-1)
Use variation of parameters to find a general solution to the differential equation given that the functions y, and y2 are linearly independent solutions to the
corresponding homogeneous equation for t> 0.
ty'"' + (6t-1)y' -6y=7t² e-6t.
Y₁ = 6t-1,
V/₂=e-6t
C
7
7
- 6t
A general solution is y(t) = c₁ (6t-1) + C₂ e
31 (21² - ²) (0-2)
(6t-1)-
1296
36
A
+
(-6e-6₁-e
6t
Transcribed Image Text:Use variation of parameters to find a general solution to the differential equation given that the functions y, and y2 are linearly independent solutions to the corresponding homogeneous equation for t> 0. ty'"' + (6t-1)y' -6y=7t² e-6t. Y₁ = 6t-1, V/₂=e-6t C 7 7 - 6t A general solution is y(t) = c₁ (6t-1) + C₂ e 31 (21² - ²) (0-2) (6t-1)- 1296 36 A + (-6e-6₁-e 6t
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