Solve the differential equation subject to the indicated initial conditions. y" – 2 y' + 5 y = 1+t, y(0) = 0 , y' (0) = 4. y (0) = 0 O y (t) = + 흉t-끓e cos(2t) + 뚫et sin(2t) 7 51 O y(t) = 끓t+-끓e cos(26) + 뚫e sin(2t) 7 51 et cos(2t) + e sin(2t) + 1은 + = 끓 +흉t + 끓e cos(2t)-뚫et sin(2t) O y (t) = - 등 -습sin(2t)-뚫 cos(2t) 7 7 O y (t) et cos(2t) | | 5 15
Solve the differential equation subject to the indicated initial conditions. y" – 2 y' + 5 y = 1+t, y(0) = 0 , y' (0) = 4. y (0) = 0 O y (t) = + 흉t-끓e cos(2t) + 뚫et sin(2t) 7 51 O y(t) = 끓t+-끓e cos(26) + 뚫e sin(2t) 7 51 et cos(2t) + e sin(2t) + 1은 + = 끓 +흉t + 끓e cos(2t)-뚫et sin(2t) O y (t) = - 등 -습sin(2t)-뚫 cos(2t) 7 7 O y (t) et cos(2t) | | 5 15
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 17E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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Transcribed Image Text:Solve the differential equation subject to the indicated initial conditions.
y" – 2 y' + 5 y = 1+t,
y (0) = 0 , y'(0) = 4.
%3|
O y(t) = +t - e cos(2t) + et sin(2t)
7
51
- et cos(2t) +
O y (t) = t + - et cos(2t) + e sin(2t)
7
1
7
51
5
O y (t) = +t + e' sin(2t)
7
7
51
et cos(2t) –
O y (t) =D -등 -습 sin(2t) - 뚫 cos(2t)
15
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