Question #182084

d²y/dx²+dy/dx+2y=0


1
Expert's answer
2021-04-20T03:52:51-0400

y+y+2y=0Auxiliary equation ism2+m+2=0m=1±i72y=ex2(Acos(72x)+Bsin(72x))\displaystyle y'' + y' + 2y = 0\\ \textsf{Auxiliary equation is}\\ m^2 + m + 2 = 0\\ m = \frac{-1 \pm i\sqrt{7}}{2}\\ \therefore y = e^{-\frac{x}{2}}\left(A\cos\left(\frac{\sqrt{7}}{2}x\right) + B\sin\left(\frac{\sqrt{7}}{2}x\right)\right)


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