Find the general solution of the differential equation
$x^2y'' + xy' + (2x^2-4)y = 0$
Answer: $y = C \sum_{n=m}^{\infty} C_n x^n$, where
$C_n = $ ____, if $n \geq m$ and $n=2k$ is even
$C_n = $ ____, if $n \geq m$ and $n=2k+1$ is odds
$m = $ ____, and $C$ is an arbitrary constant
For the differential equation $(x^2-16)^2 y'' + (x-4)y' + y = 0$
Classify the points $x=-4$, $x=0$ and $x=4$
What differential equation should be
Which series would this solution differential equation
use?, Taylor so or frobenius.
Find two linearly independent solutions of $2x^2y'' - xy' + (5x+1)y = 0$, $x>0$ of the form
$y_1 = x^{r_1}(1 + a_1x + a_2x^2 + a_3x^3 + ...)$
$y_2 = x^{r_2}(1 + b_1x + b_2x^2 + b_3x^3 + ...)$
where $r_1 > r_2$
Solve the initial values problem
$(2+x^2)y'' + y = 0$, $y(0) = 0$, $y'(0) = 10$
Find $c_0, c_1, c_2, c_3, c_4, c_5, c_6, C$
