Homework # 5 - Math 328
The problems on this homework must be done alone. The honor code is in effect.
First name: Last name:
1. Solve the following differential equation \(e^y + 2x + (xe^y + 3y^2)y'=0\).
b. \(e^{xy} + 2x + 3y = c\)
b. \(xe^{y} + x^2 + y^3 = c\)
c. \(e^{xy} + 2x + 3y^2 = c\)
d. \(\frac{x^2}{2}e^{y} + 2x + 2y^3 = c\)
e. This equation has no solution.
2. Find an integratng factor \(\mu\) to make the equation \(3x^2y + 2xy + 2y^3 + (x^2 + 2y^2)y' = 0\) exact.
b. \(\mu(x) = 3x^2y\)
b. \(\mu(x) = 3\)
c. \(\mu(x) = 3x\)
d. \(\mu(x) = e^{3x}\)
e. \(\mu(x) = 3^x\)
3. Solve the differential equation \(y'' - y' - 2y = 0\).
b. \(y(t) = c_1 e^t + c_2 e^{2t}\)
b. \(y(t) = c_1 e^{-t} + c_2 e^{2t}\)
c. \(y(t) = c_1 e^t + c_2 e^{-2t}\)
d. \(y(t) = c_1 e^{-t} + c_2 e^{-2t}\)
4. Write out and submit your solution for questions 1-3.
5. Use the integrating factor you found in question 2 to solve the differential equation.