Consider the differential equation for the function y, ty = 4y² + ty+ 16t², (a) Transform the differential equation above for y into a separable equation for u(t) v' (t) = Σ t> 1. Σ = y(t) t You should get an equation v' = f(t, v). Note: In your answer type v for u(t), and t for t. (b) Find an implicit expression of all solutions y of the differential equation above, in the form y(t, v) = c, where c collects all constant terms. (So, do not include any c in your answer.) y(t, v) = Note: In your answer type v for u(t), and t for t.
Consider the differential equation for the function y, ty = 4y² + ty+ 16t², (a) Transform the differential equation above for y into a separable equation for u(t) v' (t) = Σ t> 1. Σ = y(t) t You should get an equation v' = f(t, v). Note: In your answer type v for u(t), and t for t. (b) Find an implicit expression of all solutions y of the differential equation above, in the form y(t, v) = c, where c collects all constant terms. (So, do not include any c in your answer.) y(t, v) = Note: In your answer type v for u(t), and t for t.
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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Transcribed Image Text:Consider the differential equation for the function y,
t²y = 4y² +ty + 16 t²,
v' (t) =
y(t)
(a) Transform the differential equation above for y into a separable equation for u(t) =
t
Σ
t≥ 1.
M
You should get an equation v' = f(t, v).
Note: In your answer type v for u(t), and t for t.
(b) Find an implicit expression of all solutions y of the differential equation above, in the form y(t, v) : = c, where c collects all constant terms.
(So, do not include any c in your answer.)
y(t, v) =
Note: In your answer type v for u(t), and t for t.
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