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..
Hello, holly123!
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: .$\displaystyle y \:=\:C(x+2)^3$