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Homework-1-s11 - AMS 361 Applied Calculus IV(DE BVP...

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1 AMS 361: Applied Calculus IV (DE & BVP) Homework 1 Assignment Date: Wednesday (02/02/2011) Collection Date: Wednesday (02/16/2011) 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 . 𝑥 2 𝑦 ′′ + 𝑥𝑦 − 𝑦 = ln 𝑥 ; 𝑦 1 = 𝑥 − ln 𝑥 , 𝑦 2 = 1 𝑥 ln 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. 𝑒 𝑦 𝑦 = 1; 𝑦 ( 𝑥 ) = ln( 𝑥 + 𝐶 ) , 𝑦 (0) = 0 Problem 1-3: Find a function
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