Question

The general solution to the second-order differential equation d2ydt2−4dydt+7y=0${\displaystyle \frac{d^{2}y}{d{t}^2}-4\frac{dy}{dt}+7y=0}$ is in the form y(x)=eαx(c1cosβx+c2sinβx).${\displaystyle y(x)=e^{\alpha x}(c_1\cos \beta x+c_2\sin \beta x).}$ Find the values of α$\alpha$ and β,$\beta ,$ where β>0.$\beta >0.$

Answer: α=$\alpha =$  and β=$\beta =$

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Answer 1

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