Solution by Integrating Factor/Examples
Jump to navigation
Jump to search
Examples of Use of Solution by Integrating Factor
Example: $y' - 3 y = \sin x$
- $\dfrac {\d y} {\d x} - 3 y = \sin x$
has the general solution:
- $y = \dfrac 1 {10} \paren {3 \sin x - \cos x} + C e^{3 x}$
Example: $y' + y = \dfrac 1 x$
Consider the linear first order ODE:
- $(1): \quad \dfrac {\d y} {\d x} + y = \dfrac 1 x$
with the initial condition $\tuple {1, 0}$.
This has the particular solution:
- $y = \ds e^{-x} \int_1^x \dfrac {e^\xi \rd \xi} \xi$