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

Find the general solution of y''-4y=0.

1. y = C1 2 x + C2 2 x
2. y = C1 e2 x + C2 e- 2 x
3. y = ≤ft(C1 + C2 x ) e2 x
4. y = C1 e4 x + C2 e- 4 x

Answer

B. y = C1 e2 x + C2 e- 2 x

Solution

r2-4=0 r= 2, so y=C1e2x+C2e-2x.

More Second-Order Linear Homogeneous Equations questions

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

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