d²y/dx²+dy/dx+2y=0
y′′+y′+2y=0Auxiliary equation ism2+m+2=0m=−1±i72∴y=e−x2(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)y′′+y′+2y=0Auxiliary equation ism2+m+2=0m=2−1±i7∴y=e−2x(Acos(27x)+Bsin(27x))
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments