Introduction to Differential Equations - Self Quiz Solutions 2 | MATH 220, Study notes of Differential Equations

Download Introduction to Differential Equations - Self Quiz Solutions 2 | MATH 220 and more Study notes Differential Equations in PDF only on Docsity! MATH 220 Self-quiz 2 1. Solve the differential equation: y′ = x ln x (I know we have not started solving differential equations yet, but shouldn’t you be able to solve this one anyway? Solution: Translated into words, this differential equation seeks an an- tiderivative for the function x ln x. Thus, its solution is going to be: ∫ x ln x dx We compute this integral by an integration by parts:∫ x ln x dx = ∫ ( x2 2 )′ ln x dx = x2 2 ln x − ∫ x2 2 (ln x)′ dx = x2 2 ln x − ∫ x2 2 · 1 x dx = x2 2 ln x − x 2 4 + C Thus the solution of the give differential equation is: y = x2 2 ln x − x 2 4 + C 2. Is the function y = xex a solution of the differential equation: