Integrating factor method
Differential equations (introductory) · Mathematics
Study notes
Q: Solve dy/dx - (1/x)y = x^2 using the integrating factor method step by step. P(x) = -1/x. IF = e^(integral -dx/x) = e^(-ln x) = 1/x. Multiply: (1/x)dy/dx - y/x^2 = x, so d/dx[y/x] = x. Integrate: y/x = x^2/2 + C. Solution: y = x^3/2 + Cx.