Using the integrating factor method, find the general solution to dy/dx + (2/x)*y = 4x for x > 0.
Answer and explanation
Correct answer: D. y = x^2 + C / x^2
- Step 1: Integrating factor is I(x) = e^(integral(2/x dx)) = e^(2ln(x)) = x^2. Step 2. Multiply through: d/dx[x^2 y] = 4x^3. Integrate: x^2 y = x^4 + C => y = x^2 + C/x^2. Answer: y = x^2 + C / x^2. Why not the others:* The integrating factor must divide the entire right hand side constant.
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