Final Exam CSULB – Math 370A Spring XXXXXXXXXXName: Answer each question based on what you learn in the lectures or the textbook. Using outside resources will not give you any credit. No work is...

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Final Exam CSULB – Math 370A Spring 2021 Name: Answer each question based on what you learn in the lectures or the textbook. Using outside resources will not give you any credit. No work is needed for number 1 through 8. Work independently! 1: (8pts) Consider a first order nonlinear differential equation. Name two methods covered in class that may be used to solve such a D.E.? 2: (8pts) Consider a second order linear differential equation where the righthand side (the non- homogenous term) is tan x . What method covered in class can be used to solve such a D.E.? 3: (8pts) Consider a second order constant coefficients linear differential equation where the righthand side is 2 cost t . What method covered in class can be used to solve such a D.E. if you do not want to do any integration? 4: (8pts) Consider the second order differential equations ( ) ( ) ( )y p t y q t y g t + + = . If 2 3e t tand e− are the general solution to the corresponding homogeneous D.E. and cos t is a particular solution to the above D.E., what is the general solution to the above D.E.? 5: (8pts) In the equation for a spring mass system, what is the physical meaning of the coefficients in front of u ? 6: (8pts) Consider a spring mass equation that involves all three terms , ,u u u  (second derivative of u). Let say u is a solution. What is the limit of u as time goes to infinity? 7: (8pts) You are given a matrix and want to know if that matrix has an inverse. Before investing your time and energy trying to find the inverse, what must you first verify to ensure the matrix does have an inverse? 8: (8pts) If the matrix A does have an inverse, what do you first write down in finding the inverse if you are using row reductions? 9: (16pts) A tank with a capacity of 300 gallons originally contains 100 gallons of water with 25 pounds of salt. Water containing 2 pound of salt per gallon is entering at a rate of 5 gallon per minute. The well- stirred mixture flows out of the tank at a rate of 1 gallon per minute. How long will it take for the tank to reach its full capacity? 10. (20pts) Find a particular solution to the non-homogenous system 2 1 3 2 t t e e −     = +    − −    x x . To help with the computation use ( ) 3 t t t t e e t e e − −   =     Ψ .
Answered 4 days AfterMay 08, 2021

Answer To: Final Exam CSULB – Math 370A Spring XXXXXXXXXXName: Answer each question based on what you learn in...

Himanshu answered on May 13 2021
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