Problem 7. A Bernoulli equation is a particular kind of first order ODE that can be written in the form x'(t) = a(t)x+ g(t)x" where some integer n #1, and a(t) are some suitably integrable functions. Using the substitution y(x) = x¹-n, we can actually rewrite this equation as an ODE involving the dependent variable y instead. Use this technique to solve the initial value problem x' (t) = 2 2t -x+ 3t X x(1) = 2 Hint: when rewriting the equation using your substitution, you should find a way to use the substitution so that the variable x does not appear at all-it should only contain y and t as variables. Once you find a solution, you should reexpress it in terms ofx and t. "

Problem 7. A Bernoulli equation is a particular kind of first order ODE that can be written in the form x'(t) = a(t)x+ g(t)x" where some integer n #1, and a(t) are some suitably integrable functions. Using the substitution y(x) = x¹-n, we can actually rewrite this equation as an ODE involving the dependent variable y instead. Use this technique to solve the initial value problem x' (t) = 2 2t -x+ 3t X x(1) = 2 Hint: when rewriting the equation using your substitution, you should find a way to use the substitution so that the variable x does not appear at all-it should only contain y and t as variables. Once you find a solution, you should reexpress it in terms ofx and t. "

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 5CR

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