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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 y' = (t + y)² – 1, y(3) = 5. (a) g(z) =| help (formulas) (b) y(t) =help (formulas)

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 y' = (t + y)² – 1, y(3) = 5. (a) g(z) =| help (formulas) (b) y(t) =help (formulas)

Advanced Engineering Mathematics
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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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. = f(at + By + y), where a, ß, and y are constants. Use the change of variable z = at + ßy +Y 1. Consider a differential equation of the form y' to rewrite the differential equation as a separable equation of the form z' = g(z). Solve the initial value problem y' = (t + y)² – 1, y(3) = 5. (a) g(z) = help (formulas) (b) y(t) = help (formulas)
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. = f(at + By + y), where a, ß, and y are constants. Use the change of variable z = at + ßy +Y 1. Consider a differential equation of the form y' to rewrite the differential equation as a separable equation of the form z' = g(z). Solve the initial value problem y' = (t + y)² – 1, y(3) = 5. (a) g(z) = help (formulas) (b) y(t) = help (formulas)
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