Which of the following is true for y(x) that satisfies the differential equation dy/dx = xy - 1 + x - y; y(0) = 0

Question

Which of the following is true for y(x) that satisfies the differential equation

\(\frac{dy}{dx}=xy - 1 + x - y;\, y(0)=0:\)

(1) \(y(1) = e^{-\frac{1}{2}}-1\)

(2) \(y(1) = e^{\frac{1}{2}}-e^{\frac{1}{2}}\)

(3) \(y(1) = 1\)

(4) \(y(1) = e^{\frac{1}{2}}-1\)

Answer 1

Correct answer is (1)