Texts: Same section, please help with the marked questions. 10, 12, 18, 20. Please keep the solutions short and to the point! Thanks.
In each of Problems 1-6, find a general solution using:
11. y'' - 6y' + 8y = 3e^x
Solution of the nonhomogeneous equation.
13. y''' + 2y' = 10sin(x)
1. y + y' = tan(x)
14. y'''' = 8x + 2e^x
2. y'' - 4y' + 3y = 2cos(x) + 3
15. y'''' + 13y''' = 5e^x
3. y + 9y' = 12sec^3(x)
16. y'' + y' = 3r + 25sin(3x)
4. y = 2y' - 3y = 2sin(x)
In each of Problems 17-24, solve the initial value problem.
5. y' - 3y' + 2y = cos(e^(-x))
6. y' - 5y' + 6y = 8sin(4x)
17. y'''' = -7e^x + xy'' = 1, y(0) = 3
In each of Problems 7-16, find a general solution using the method of undetermined coefficients for a particular solution of the nonhomogeneous equation.
18. y' + 4y = 8 + 34cos(x), y(0) = 3
19. y' + 8y' + 12y = e^x + 7, y(0) = 1, y'(0) = 2
20. y''' + y = 2esin(x), y(0) = 2
22. y''y' + y = 1, y(1) = 4, y'(-2) = -2
23. y''y = 5sin(x), y(0) = 2, y'(0) = -4
24. y' + y = tan(x), y(0) = 4, y'(0) = 3
10. y'' - 4y' + 5y = 21e^x
