(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

d2u/d2x + 1/2Lu = 0 where L is function of x

2. Relevant equations

I am try to find solutions y1 and y2 of this equation.

3. The attempt at a solution

y = [cos √(L/2) x] + [sin √(L/2) x]

y' = - [√(L/2) sin √(L/2) x] + [ √(L/2) cos √(L/2) x]

y'' = -[(L/2) cos √(L/2) x] - [(L/2) sin √(L/2) x ]

so now we have

y = [cos √(L/2) x] + [sin √(L/2) x]

and if we multiply it with (1/2 L ) we get negative y'' which will satisfy original equation.

so solutions are

y1 = cos √(L/2) x

y2 = sin √(L/2) x

is that correct ?

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# Homework Help: Second order ODE: finding solution.

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