Solution by Integrating Factor/Examples/y' - 3y = sin x

Theorem
The linear first order ODE:
 * $\dfrac {\d y} {\d x} - 3 y = \sin x$

has the general solution:
 * $x y = x \sin x + \cos x + C$

Proof
This is a linear first order ODE in the form:
 * $\dfrac {\d y} {\d x} + \map P x y = \map Q x$

where:
 * $\map P x y = -3 y$
 * $\map Q x = \sin x$

Thus:

Thus from Solution by Integrating Factor: