Solve the first-order linear ODE y' + y = e^{2x} with y(0) = 1. Which is the correct solution?

Solve the first-order linear ODE y' + y = e^{2x} with y(0) = 1. Which is the correct solution?

• A. y = (1/3) e^{2x} + (2/3) e^{-x}
• B. y = e^{2x} - e^{-x}
• C. y = (1/2) e^{2x} + (1/2) e^{-x}
• D. y = (2/3) e^{2x} - (1/3) e^{-x}

Answer: (A)