Mathematics: What is the length of each side? label each side with an expression that represents its length

What is the length of each side? label each side

richardcarmona54

27.10.2022

We're told that the ODE

x^2y''-5xy'+8y=24

has solution

y=C_1x^2+C_2x^4+3

a. If y(-1)=0 and y(1)=8 , then

$\begin{cases}0=C_1+C_2+3\\8=C_1+C_2+3\end{cases}$

but there is no solution to this system, so a member cannot be found.

b. If y(0)=8 and y(1)=5 , then

$\begin{cases}8=3\\5=C_1+C_2+3\end{cases}$

but the first equation is obviously false, so a member cannot be found.

c. If y(0)=3 and y(1)=0 , then

$\begin{cases}3=3\\0=C_1+C_2+3\end{cases}$

which has infinitely many solutions for C_1,C_2 , so a member can be found.

d. If y(1)=3 and y(2)=15 , then

$\begin{cases}3=C_1+C_2+3\\15=4C_1+256C_2+3\end{cases}\implies C_1=-\dfrac5{84},C_2=\dfrac5{84}$

so a member can be found.

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