y'' - 2y' + y = e^x arctan x where y(0) = 0, y'(0) = 1. Please solve all the way, including initial conditions.
Added by Tom-S H.
Step 1
We can solve this by finding the characteristic equation: r^2 - 2r + 1 = 0. This equation factors as (r - 1)^2 = 0, so r = 1 is a repeated root. Therefore, the complementary function is given by: y_c(x) = C_1 e^x + C_2 xe^x Show more…
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