find a general solution to the differential equation

(2+x) dy/dx = 3y

i got the answer y= 6+3x+e^(3c)

but i don't think that makes much sense..

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- Jan 5th 2009, 11:21 AMholly123sorry, another differential equation
find a general solution to the differential equation

(2+x) dy/dx = 3y

i got the answer y= 6+3x+e^(3c)

but i don't think that makes much sense.. - Jan 5th 2009, 11:25 AMJester
- Jan 5th 2009, 11:27 AMholly123
okay thats what i got but i didn't know how to solve for y. i know you have to inject e to cancel out ln

so would it be y= 3(2+x) + e^(3c)

im not sure - Jan 5th 2009, 11:31 AMJester
- Jan 5th 2009, 11:38 AMSoroban
Hello, holly123!

Quote:

Find a general solution to the differential equation: .$\displaystyle (2+x)\frac{dy}{dx} \:= \:3y$

i got the answer: .$\displaystyle y\:=\: 6+3x+e^{3c}$

but i don't think that makes much sense. . . . . no, it doesn't

Separate the variables: .$\displaystyle \frac{dy}{y} \:=\:\frac{3\,dx}{x+2}$

Integrate: .$\displaystyle \int\frac{dy}{y} \:=\:3\int\frac{dx}{x+2} \quad\Rightarrow\quad \ln y \:=\:3\ln(x+2) + c$

. . $\displaystyle \ln y \:=\:\ln(x+2)^3 + \ln C \quad\Rightarrow\quad \ln y \:=\:\ln\bigg[C(x+2)^3\bigg] $

Therefore: .$\displaystyle y \:=\:C(x+2)^3$

- Jan 5th 2009, 11:44 AMholly123
thank you