In this problem, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solut
ion of the second-order IVP consisting of this differential equation and the given initial conditions. x(π/4) = 2 2 , x'(π/4) = 0
1 answer:
Differentiate the given solution:

Now, given that <em>x</em> (<em>π</em>/4) = √2/2 … (I'm assuming there are symbols missing somewhere) … you have



Similarly, given that <em>x'</em> (<em>p</em>/4) = 0, you have



From this result, it follows that

So the particular solution to the DE that satisfies the given conditions is

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