Sometimes a change of variable can be used convert a differential equation y' = f(t, y) into a separable equation. One common change of variable technique is as follows. 1. Consider a differential equation of the form y' = f(at + By + y), where a, ß, and y are constants. Use the change of variable z = at +By+y to rewrite the differential equation as a separable equation of the form z' = g(z). Solve the initial value problem (a) g(z) = (b) y(t) = y' = (t + y)² − 1, y(2) = 4. help (formulas) help (formulas)
Sometimes a change of variable can be used convert a differential equation y' = f(t, y) into a separable equation. One common change of variable technique is as follows. 1. Consider a differential equation of the form y' = f(at + By + y), where a, ß, and y are constants. Use the change of variable z = at +By+y to rewrite the differential equation as a separable equation of the form z' = g(z). Solve the initial value problem (a) g(z) = (b) y(t) = y' = (t + y)² − 1, y(2) = 4. help (formulas) help (formulas)
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:Sometimes a change of variable can be used to convert a differential equation y' = f(t, y) into a separable
equation. One common change of variable technique is as follows.
1. Consider a differential equation of the form y' = f(at +By+y), where a, ß, and y are constants. Use the
change of variable z = at + By + y to rewrite the differential equation as a separable equation of the form
z' = g(z).
Solve the initial value problem
(a) g(z) =
=
(b) y(t) =
y' = (t + y)² −1, y(2) = 4.
help (formulas)
help (formulas)
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