How to solve
For a first-order linear ODE y' + P(x)y = Q(x), the integrating factor μ(x) = e^(∫P dx) turns the left side into an exact derivative (μy)'. When P is constant, that factor is simply e^(Px).
Steps
- Identify the constant coefficient P in y' + Py = Q.
- Form μ(x) = e^(∫P dx) = e^(Px).
- Enter μ only (not the full solution).
Example
Find μ(x) for y' + 2y = x.
- P = 2 is constant.
- μ(x) = e^(∫2 dx) = e^(2x).
Answer: e^(2x)
How to type answers
- Enter like e^(2x)
Loading drills…