H2 Maths 5.5 - Differential Equations: First-Order Linear (Integrating Factor)

What you will learn

• Solve dy/dx + (2/x) y = x^2 in standard form dy/dx + P(x) y = Q(x), with y(1) = 2.
• Integrating factor mu(x) = exp(integral P dx) = exp(2 ln x) = x^2.
• Multiply through: d/dx (x^2 y) = x^4; integrate to x^2 y = x^5 / 5 + C, so general y = x^3 / 5 + C / x^2.