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Homework-1-f11 - AMS 361 Applied Calculus IV Homework 1...

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AMS 361: Applied Calculus IV Homework 1 Assignment Date: Thursday (09/08/2011) Collection Date: Thursday (09/15/2011) 5:35pm Grade: Each problem is worth 10 points. Problem 1-1: Verify by substitution that the given functions are solutions of the given differential equation. Primes denote derivatives with respect to x . 𝑦 ′′ + 25 𝑦 = 0; 𝑦 1 = cos 5 𝑥 , 𝑦 2 = sin 5 𝑥 Problem 1-2: Verify that y(x) satisfies the given differential equation and then determine a value of the constant c so that y(x) satisfies the given initial condition. 𝑦 + 3 𝑥 2 𝑦 = 0; 𝑦 ( 𝑥 ) = 𝐶 exp( −𝑥 3 ) , 𝑦 (0) = 7 Problem 1-3: Find a function ( ) y f x = satisfying the given differential equation and the
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