Review of first-order methods
General · Mathematics
Study notes
Q: Solve y' + 2xy = x (linear first-order). Integrating factor: μ = e^∫2xdx = e^(x²). (e^(x²)y)' = xe^(x²). e^(x²)y = ∫xe^(x²)dx = e^(x²)/2 + C. y = 1/2 + Ce^(-x²)! Check: y' = -2xCe^(-x²); y'+2xy = x ✓!