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Consider the equation ay'' + by' + cy = d, where a, b, c, and d are constants. (a) find all equilibrium, or constant, solutions of this differential equation. (enter your answers as a comma-separated list of equations.)

Respuesta :

wizard123
Rewrite equation so that it is homogeneous . 
[tex]ay'' +by' + cy = 0[/tex]

Solve characteristic equation:
[tex]ar^2 +br + c = 0 \\ \\ r = \frac{(-b) \pm \sqrt{b^2 -4ac}}{2a}[/tex] 

The solutions to the homogeneous equation are:
[tex]y = k_1 e^{r_1 t} + k_2 e^{r_2 t}[/tex]

Finally you need the constant term in "cy" to equal 'd' to satisfy the particular solution.
[tex] y= k_1 e^{r_1 t} + k_2 e^{r_2 t} + \frac{d}{c}[/tex]

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