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

Question

10404 views around the world

You can reuse this answer
Creative Commons License

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#