(Solved):   Answer is provided. Cauchy-Euler ODE Find the general solution to the given Euler equation ...

 

Answer is provided. Cauchy-Euler ODE

Find the general solution to the given Euler equation on \( (0, \infty) \). Use \( c_{-} 1 \) and \( c_{-} 2 \) for your coefficients. \[ x^{2} y^{\prime \prime}+7 x y^{\prime}+13 y=0 \] \[ y= \] TIP Enter your answer as an expression. Example: \( 3 \mathrm{x}^{\wedge} 2+1, \mathrm{x} / 5,(\mathrm{a}+\mathrm{b}) / \mathrm{c} \) Be sure your variables match those in the question Get Help: \[ x^{-3}\left(c_{1} \cos (2 \ln (x))+c_{2} \sin (2 \ln (x))\right) \]