Solve: y” + y’ = 0, y(0) = 5, y(π/4) = 3

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Solution:

Here, The auxiliary equation is

m2 + m = 0

Solving this equations,

m = 0 and m = -1

Here, roots are real and unequal.

Hence the general solution is

y = C1e0.x + C2e-1.x

y = C2e-x

Applying condition y(0) = 5 and y(π/4) = 3

5 = C2

The particular solution of the given equation y = 5e-x

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