Consider the initial value problem for the function y given by y – 3y(1 -). y(0) = 3. (a) Find an implicit expression of all solutions y of the differential equation above, in the form (t, y) = c, where c collects all constant terms. (So, do not include any c in your answer.) Þ(t, y) = | 3t + 1/4ln(3) - In(y/(4-y)) Σ K 1 1 Hint: Recall the partial fraction decomposition where K is any constant. y (K – y) (К — у) (b) Find the explicit expression of the solution y of the initial value problem above. y(t) = (In(3))/(e^(-3t) + (1/4)ln(3)) Σ
Consider the initial value problem for the function y given by y – 3y(1 -). y(0) = 3. (a) Find an implicit expression of all solutions y of the differential equation above, in the form (t, y) = c, where c collects all constant terms. (So, do not include any c in your answer.) Þ(t, y) = | 3t + 1/4ln(3) - In(y/(4-y)) Σ K 1 1 Hint: Recall the partial fraction decomposition where K is any constant. y (K – y) (К — у) (b) Find the explicit expression of the solution y of the initial value problem above. y(t) = (In(3))/(e^(-3t) + (1/4)ln(3)) Σ
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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I need help finding the explicit form of the equation. I already found the correct implicit form.
Transcribed Image Text:Consider the initial value problem for the function y given by
y – 3y(1 -).
y(0) = 3.
(a) Find an implicit expression of all solutions y of the differential equation above, in the form (t, y) = c, where c collects all constant terms. (So, do
not include any c in your answer.)
Þ(t, y) = | 3t + 1/4ln(3) - In(y/(4-y))
Σ
K
1
1
Hint: Recall the partial fraction decomposition
where K is any constant.
y (K – y)
(К — у)
(b) Find the explicit expression of the solution y of the initial value problem above.
y(t) =
(In(3))/(e^(-3t) + (1/4)ln(3))
Σ
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