Engineering Board Exam Reviewer · Second-Order Linear Homogeneous Equations · medium

Find the general solution of y'''-3y''+2y'=0.

1. y = C1 + C2 e- x + C3 e- 2 x
2. y = C1 ex + C2 e2 x + C3 e3 x
3. y = C1 + C2 ex + C3 x ex
4. y = C1 + C2 ex + C3 e2 x

Answer

D. y = C1 + C2 ex + C3 e2 x

Solution

r3-3r2+2r=r(r-1)(r-2)=0 r=0,1,2. Hence y=C1+C2ex+C3e2x.

More Second-Order Linear Homogeneous Equations questions

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

All Second-Order Linear Homogeneous Equations questions