Final answer:
To find the general solution of the given differential equation y' = 2y - 4x, use the method of integrating factors.
Step-by-step explanation:
The given differential equation is y' = 2y - 4x. To find the general solution, we can use the method of integrating factors.
Step 1: Write the equation in the form dy/dx + P(x)y = Q(x), where P(x) = -2 and Q(x) = -4x.
Step 2: Find the integrating factor, which is given by the formula κ(x) = e∫[2P(x)dx]. In this case, the integrating factor is e∫(-4x)dx = e-2x2.
Step 3: Multiply both sides of the equation by the integrating factor and integrate. The general solution is given by y(x) = e∫(-4x)dx * (∫Q(x)e∫(4x)dx + C), where C is the constant of integration.