Question

(2+x) dy/dx=3y How do I solve this with separation of variables?

Answer 1

(2+x)dy/dx = 3y

(1/3y)dy = 1/(2+x) dx
(1/3)ln(y) = ln(x+2) + c

Answer 2

\[(2+x) \frac { dy} {dx}=3y\] can be rearranged to:
\[\frac{ dy }{ 3y } = \frac{ dx }{(2+x) }\]

Answer 3

(1/3)ln(y) = ln(x+2) + c

ln(y) = 3*ln(x+2) + c ; c*3 is just another constant c

y = e^(3*ln(x+2) + c)

y = e^ln((x+2)^3) *e^c

y = (x+2)^3 *e^c

// e^c is just another constant c

y = (x+2)^3 *c

Answer 4

Don't you need to integrate somewhere?

Answer 5

// sorry i didn't show it explicitly
(1/3y)dy = 1/(2+x) dx

// here i integrated.
(1/3)ln(y) = ln(x+2) + c

Answer 6

Oh ok. Thanks. Makes more sense. I kind of caught it, but I wanted to make sure.

Answer 7

\[\int\limits \frac{ dy }{ 3y } = \int\limits \frac{ dx }{(2+x) }\] do you know how to integrate from here: \[\frac{ 1 }{ 3 } \int\limits \frac{ 1 }{ y } dy = \int\limits \frac{ 1}{(2+x) } dx\]