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

Find the general solution of y''-5y'+6y=0.

1. y = C1 e2 x + C2 e3 x
2. y = C1 e- 2 x + C2 e- 3 x
3. y = C1 ex + C2 e6 x
4. y = ≤ft(C1 + C2 x ) e5 x/2

Answer

A. y = C1 e2 x + C2 e3 x

Solution

The characteristic equation r2-5r+6=0 gives (r-2)(r-3)=0, so r=2,3. Hence y=C1e2x+C2e3x.

More Second-Order Linear Homogeneous Equations questions

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 ).
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8. Find the general solution of y''+2y'+5y=0.
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