What is a general solution to the differential equation $y'-3y=5$ ?

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Answer 1 · 2016-06-26T06:37:47

$= gamma e^ {3x} - 5/3$

$y'-3y=5$

$y'= 3y+5$

$(y')/(3y+5) =1$

$int \ (dy)/(3y+5) =int \ dx$

$1/3ln(3y+5) =x + alpha$

$ln(3y+5) =3( x + alpha)$

$3y+5 = e^ {3( x + alpha)} = e^ {3x} e^ {3 alpha} = beta e^ {3x}$

$y = 1/3 ( beta e^ {3x} - 5)$

$= gamma e^ {3x} - 5/3$

What is a general solution to the differential equation y'-3y=5y'-3y=5?