First-order linear equation and integrating factor (Linear in y: dy/dx + P(x)y = Q(x). Multiply by IF = exp(∫P dx) so left)
jee-mainjee-advanced
Linear in y: dy/dx + P(x)y = Q(x). Multiply by IF = exp(∫P dx) so left side becomes d/dx(y·IF); integrate to solve.
What each symbol means
| Symbol | What it stands for |
|---|---|
| IF | Integrating factor e^{∫P dx}. |
| P(x) | Coefficient of y. |
| Q(x) | Nonhomogeneous term. |
When to use this
Standard form must have coefficient 1 on dy/dx (divide through if needed).