Q: Solve dy/dx + 2xy = x. Standard form with P(x) = 2x, Q(x) = x. IF = e^(integral 2x dx) = e^(x^2). Multiply: d/dx[y e^(x^2)] = x e^(x^2). Integrate: y e^(x^2) = e^(x^2)/2 + C. Solution: y = 1/2 + C e^(-x^2).