Find the general solution by separating the variables then integrating: dy / dx = cosx℮^(y + sinx) dy / dx = cosx℮ʸ℮^(sinx) ℮^(-y) dy = cosx℮^(sinx) dx ∫ ℮^(-y) dy = ∫ cosx℮^(sinx) dx -℮^(-y) = ℮^(sinx) + C ℮^(-y) = C - ℮^(sinx) -y = ln[C - ℮^(sinx)] y = -ln[C - ℮^(sinx)]
Find the particular solution by solving for the constant: When x = 0, y = 0 -ln(C - 1) = 0 ln(C - 1) = 0 C - 1 = 1 C = 2 <span>y = -ln[2 - ℮^(sinx)]
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