Ordinary differential equations (first and higher order)
Engineering Mathematics · Engineering
Study notes
Solve dy/dx + 2y = 4x (first-order linear ODE). Step 1: P(x) = 2, so integrating factor μ = e^(∫2dx) = e^(2x). Step 2: Multiply: d/dx(ye^(2x)) = 4xe^(2x). Step 3: Integrate: ye^(2x) = ∫4xe^(2x)dx = (2x−1)e^(2x) + C (by parts). Step 4: y = 2x − 1 + Ce^(−2x).