Differential equations
Not what you're looking for?
See attached for formatting
1. Considering the differential equation y' = (y/x)3 :
a. Discuss existence and uniqueness of solutions.
b. Determine if exist constant solutions.
c. Determine the general integral.
d. Solve Cauchy problems y(3) = -1, y(3) = 0 and determine the maximal interval of solutions.
2) Integrate the differential equation
3) Solve the Cauchy problem:
y'' + y' = sin x
y(0) = y'(0) = 0
4. Calculate the volume of cylinder with generatrix parallel to z axis included between T domain = and the part of surface of equation z = log(xy) , projected on T.
5.
The integral ... where T is the square with vertex (0,1) , (1,0), (0,-1), (-1,0)
A. Is equal to the area of the square
B. Is ½ of the area of the square
C. Is reducible to a multiple of an integral in the first quadrant
D. Is reducible to a multiple of an integral calculated in the first quadrant under the line y=x
E. The value can be determined without the direct calculation of the integral
Purchase this Solution
Solution Summary
This provides examples of a variety of differential equation problems, including Cauchy problems, integration, volume, and curvilinear abscissa.
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts