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Calculating the general solution of differential equation y '+ y-e ^ (- x) = 0
A solution without formula is given
General solution of differential equation E ^ y '= x
Take logarithm on both sides: y '= LNX, dy / DX = LNX, Dy = lnxdx, integral on both sides: y = x (lnx-1) + C
The general solution of the differential equation y '- y = e ^ x?
First, we integrate y = (y ^ 2) / 2 + e ^ x, and simplify y ^ 2-2y + 2E ^ x = 0
(Y-1) ^ 2 = 1-2e ^ x, so 1-2e ^ x ≥ 0, finally x ≤ root E
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