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# Help me with Differential Equations?

Solve the differential equation y"+4y=0.

r^2+4=0

r=2i, -2i

Now what?

### 2 Answers by Expert Tutors

Xavier J. | Tutor in Math, topics range from Algebra to Calculus.Tutor in Math, topics range from Algebra...
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Marked as Best Answer

When you get complex roots a ± bi, the general solution becomes y(t) = eatcos(bt) + eatsin(bt). So for this problem you get y(t) = cos(2t) + sin(2t)

Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.
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You have applied Euler's method to solve the homogeneous with constant coefficeints.

The common solution of the equation can be expressed like this:

y = C1 e rx + C2 e -rx                                                 (1)

You have found the right equation for r after substituting  (1) into you differential equation. Use

r = 2i and r = -2i

to come up with final solution:

y = C1 e 2ri  + C2 e - 2ri

This solution can be expressed in terms of trigonometric functions, but coefficients C1 and C2 have to be found from boundary conditions which are not given here.