Hello,
This exercice is very hard for me. I have found the theory in "Mathematics for students of engineering and applied science" by L.B.Benny (Oxford University Press) page 415"
[tex]x=e^t\\
\frac{dt}{dx}= \frac{1}{x}\\
x^2 \frac{d^2y}{dx^2}= \frac{d^2y}{dt^2} -\frac{dy}{dt} \\
[/tex]
[tex] \frac{d^2y}{dt^2} - \frac{dy}{dt} -7 \frac{dy}{dt} +16y=0\\
\frac{d^2y}{dt^2} -8 \frac{dy}{dt} +16y=0\\
\Delta=8^2-4*16=0\\
r=4\\
y=(a+bt)e^{4t}
==\ \textgreater \ y=(a+b\ ln(x))x^4
[/tex]
If i am wrong, forget all this.
