y 5 3 and obtain du dt 2 t u 4 9 which is a linear differential equation Joseph

# Y 5 3 and obtain du dt 2 t u 4 9 which is a linear

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y - 5 / 3 and obtain du dt - 2 t u = - 4 9 , which is a linear differential equation Joseph M. Mahaffy, h [email protected] i Lecture Notes – Exact and Bernoulli Differential — (24/26)

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Introduction Exact Differential Equations Bernoulli’s Differential Equation Logistic Growth Equation Alternate Solution Bernoulli’s Equation Example: Bernoulli’s Equation 2 Example (cont): The linear differential equation in u ( t ) is du dt - 2 t u = - 4 9 , which has an integrating factor μ ( t ) = e - 2 R dt t = e - 2 ln( t ) = 1 t 2 This gives d dt u t 2 = - 4 9 t 2 , which integrating gives u t 2 = 4 9 t + C or u ( t ) = 4 t 9 + Ct 2 Joseph M. Mahaffy, h [email protected] i Lecture Notes – Exact and Bernoulli Differential Equations — (25/26) Introduction Exact Differential Equations Bernoulli’s Differential Equation Logistic Growth Equation Alternate Solution Bernoulli’s Equation Example: Bernoulli’s Equation 3 Example (cont): However, u ( t ) = y - 2 / 3 ( t ), so if u ( t ) = 4 t 9 + Ct 2 , then y - 2 / 3 ( t ) = 4 t 9 + Ct 2 The explicit solution is y ( t ) = 9 4 t + 9 Ct 2 3 2 Joseph M. Mahaffy, h [email protected] i Lecture Notes – Exact and Bernoulli Differential — (26/26)
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