Find the general solution of the given second order differential equation. $$4y''+y'=0$$
This was my procedure to solving this problem:
$\chi(r)=4r^2+r=0$
$r(4r+1)=0$
$r=0, -\frac14$
$y_1=e^{0x}, y_2=e^{-\frac14x}$
And this led to get the answer,
$y=C_1+C_2e^{-\frac14x}$
I don't really have a question unless I solved this problem incorrectly. If someone could kindly check over my work to see if I did it right, that would be great!
2 Answers
$\begingroup$You are fine for the general solution, assuming the first term is $4y''$.
$\endgroup$ $\begingroup$hint you can reduce the order by putting
$\endgroup$$$y'=w$$
