1) This is a first-order linear differential equation. We can rewrite it in standard form as y' - xy = 2xe^(x^2). The integrating factor is e^(-1/2(x^2)), so multiplying both sides by the integrating factor gives us e^(-1/2(x^2))y' - xe^(-1/2(x^2))y = 2x. Integrating both sides with respect to x, we get the solution y(x) = e^(1/2(x^2))(C + x^2 - 2), where C is the constant of integration.

2) This is a first-order linear differential equation. We can rewrite it in standard form as y' + y = 1. The integrating factor is e^(x), so multiplying both sides by the integrating factor gives us e^(x)y' + e^(x)y = e^(x). Integrating both sides with respect to x, we get the solution y(x) = Ce^(-x) + 1, where C is the constant of integration.

3) This is a first-order linear differential equation. We can rewrite it in standard form as y' + 3y = 5x. The integrating factor is e^(3x), so multiplying both sides by the integrating factor gives us e^(3x)y' + 3e^(3x)y = 5xe^(3x). Integrating both sides with respect to x, we get the solution y(x) = Ce^(-3x) + 5/3 - 5/3 * x, where C is the constant of integration.