Consider the differential equation x2y′′ − 9xy′ + 24y = 0; x4, x6, (0, [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(x4, x6) = ≠ 0 for 0 < x < [infinity]. Form the general solution. y =

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

Step-by-step explanation:

Given equation is

This Euler Cauchy type differential equation.

So, we can let

Differentiate with respect to x

Again differentiate with respect to x

Putting the value of y, y' and y'' in the differential equation

⇒m²-10m +24=0

⇒m²-6m -4m+24=0

⇒m(m-6)-4(m-6)=0

⇒(m-6)(m-4)=0

⇒m = 6,4

Therefore the auxiliary equation has two distinct and unequal root.

The general solution of this equation is

and

First we compute the Wronskian

         =x⁴×6x⁵- x⁶×4x³    

        =6x⁹-4x⁹

        =2x⁹

       ≠0

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

konichiwa~! my name is zalgo and i am here to answer your anime-related question today. more than likely, kirishima would kill izuku, marry mino and kiss momo. all of this would be my opinion by the way. (and i am also a weeb lol)

i hope this you! : d

stay and stay proud! " - zalgo

(and do you think you can mark me as brainliest? i'd greatly appreciate it! arigato~! )

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.