Question

Find the general solution of the given second-order differential equation. 3y'' + 2y' + y = 0

Answer 1

Consider, pls, this option.
Modify solution design according own requirements.

Answer 2

The general solution will be "$y = e^{\frac{-x}{3} } (c_1 cos(\frac{\sqrt{2} }{3} x)+ (c_2 cos(\frac{\sqrt{2} }{3} x))$".

Given:

• $3y'' +2y'+y =0$

By writing it in operator form, we get

→ $(3D^2+2D+1)y =0$

Auxiliary equation will be:

→ $3m^2+2m+1=0$

The roots will be:

→ $m = \frac{-1 \pm \sqrt{4-12} }{2\times 3}$

       $= \frac{-2 \pm 2\sqrt{2}i }{2\times 3}$

       $= -\frac{1}{3} \pm \frac{\sqrt{2} }{3} i$

Thus the above answer is right.  

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