Mathematics: Use the method of indefinite coefficients and find a particle solution for differential equation: y - 5y + 5y = 3e ^ x.

Use the method of indefinite coefficients and find

hazeleyes8908

11.03.2022

Find a particle solution for differential equation in a form $y_p=a\cdot e^x,$ where a is unknown coefficient.

If $y_p=a\cdot e^x,$ then

$y_p'=(a\cdot e^x)'=a\cdot e^x,$ $y_p''=(a\cdot e^x)'=a\cdot e^x.$

Substitute these data into the differential equation:

$a\cdot e^x-5\cdot a\cdot e^x+5\cdot a\cdot e^x=3e^x,\\ \\a\cdot e^x=3e^x,\\ \\a=3.$

Thereofre, the particle solution for differential equation is

y_p=3e^x.

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mat1413

31.08.2020

wassup

Step-by-step explanation:

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