Mathematics, 20.07.2019 03:30, Renabelle6350
Use the substitution of x=e^{t} to transform the given cauchy-euler differential equation to a differential equation with constant coefficients then solve that by any method. (finding the characterristic (auxiliary) equation or variation of parameters). do not forget to re-subtitute for x after you solve the equation.
x^{2}y^{''}+9xy^{'}-20y=0
Answers: 1
.
is then a function of 
; denote this function by 
. Then by the product rule,![\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dt}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm df}{\mathrm dx}](/tpl/images/0110/2121/7213c.png)
is
and 
, so the characteristic solution is
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Use the substitution of x=e^{t} to transform the given cauchy-euler differential equation to a diffe...
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