# Consider the second order differential equation y 00

• Notes
• 14

This preview shows pages 4–8. Sign up to view the full content.

Consider the second order differential equation y 00 - 4 y 0 + 4 y = 2 e 3 x . (1) (a) Find the general solution of the homogeneous equation corresponding to (1). (b) Find a particular solution of the inhomogeneous equation (1). (c) Solve the initial value problem given by (1) and initial conditions y (0) = 0, y 0 (0) = - 1.

This preview has intentionally blurred sections. Sign up to view the full version.

EGR 265, Spring 2012, Final Exam 5 Problem 4 (12 points) A mass of 100 kg stretches an undamped spring by 10 cm. Assume that g = 10 m/s 2 . Include the correct units in all your answers below. (a) Find the spring constant k and its correct unit. (b) Set up the second order differential equation which governs the motion of the spring-mass system, choosing the x -axis to be oriented downwards. Find the general solution of this equation. (c) Find the particular solution of the equation if the mass is released 50 cm below the equilibrium position from rest. (d) What is the first positive time at which the mass returns to the equilibrium position?
EGR 265, Spring 2012, Final Exam 6 Problem 5 (10 points) (a) Find the gradient of f ( x, y ) = ye xy . (b) Evaluate the directional derivative of f ( x, y ) at the point with coordinates (0 , 1) in the direction of the vector from (0 , 1) to (1 , 3). (c) Find a unit vector in the direction of steepest increase of f ( x, y ) at the point (0 , 1).

This preview has intentionally blurred sections. Sign up to view the full version.

EGR 265, Spring 2012, Final Exam 7 Problem 6 (10 points) (a) Determine the equation of the tangent plane to the graph of z = x x + y through the
This is the end of the preview. Sign up to access the rest of the document.
• Fall '12
• Franklin
• Constant of integration, Boundary value problem

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern