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Help me with Differential Equations?

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


r=2i, -2i

Now what?

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Xavier J. | Tutor in Math, topics range from Algebra to Calculus.Tutor in Math, topics range from Algebra...
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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.

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.