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. 𝑥2𝑦′′+𝑥𝑦′− 𝑦= ln𝑥; 𝑦1=𝑥 −ln𝑥,𝑦2=1𝑥−ln𝑥Problem 1-2:Verify that y(x)satisfies the given differential equation and then determine a value of the constant cso that y(x)satisfies the given initial condition. 𝑒𝑦𝑦′= 1; 𝑦(𝑥) = ln(𝑥+𝐶) ,𝑦(0) = 0Problem 1-3: Find a function
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