Mathematics, 14.07.2020 02:01 chriscendypierre56
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. Solve the original equation by solving the new equation x2y'' + 9xy' - 20y = 0
Answers: 2
![x^2y''(x)+9xy'(x)-20y(x)=0\\ e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\ \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\ \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\](/tpl/images/0705/0951/50bae.png)
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Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation...
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