Second-Order Linear Homogeneous Equations — Engineering Board Exam Practice Questions

12 free engineering board exam reviewer questions on Second-Order Linear Homogeneous Equations (Differential Equations), each with the correct answer and a worked solution.

1. Find the general solution of x2y''-2xy'+2y=0 for x>0.
2. Find the differential equation whose general solution is y=C1ex+C2e3x.
3. Solve y''-y'-6y=0 with y(0)=0 and y'(0)=5, and find y( 2).
4. Solve y''+4y=0 with y(0)=1 and y'(0)=2, and find y≤ft( π4 ).
5. Find the general solution of y'''-3y''+2y'=0.
6. Find the general solution of 2y''+y'-y=0.
7. Find the general solution of y''-2y'+2y=0.
8. Find the general solution of y''+2y'+5y=0.
9. Find the general solution of y''+4y'+4y=0.
10. Find the general solution of y''+9y=0.
11. Find the general solution of y''-4y=0.
12. Find the general solution of y''-5y'+6y=0.