(1 point) Sometimes a change of variable can be used to convert a differential equation y'=...

Transcribed Image Text:

(1 point) 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, p, 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(2). Solve the initial value problem (a) g(z) = (b) y(t) = help (formulas) y' = (t + y)²-1, y(3) = 5. help (formulas) (1 point) 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, p, 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(2). Solve the initial value problem (a) g(z) = (b) y(t) = help (formulas) y' = (t + y)²-1, y(3) = 5. help (formulas)

Answer rating: 100% (QA)

y y t y 1 Let So Now Now So gz ty we dt have y d33 2 N 8 y 5 Z y ... View the full answer