# differential equations urgent homework!

• December 23rd 2008, 02:23 AM
GabrielKiefer
differential equations urgent homework!
Solve the differential equation y’ = y/x using the separation of variables
a. separate the variables in y’ = y/x
b. use integration to solve your equation from step a.

find the general solution of the differential equation (x^2 + 5)dy = xydx by completing the steps below.
a. separate the variables
b. integrate the resulting equation
c. solve for y
d. check by differentiation
• December 23rd 2008, 03:02 AM
Skalkaz
Hi again,

as I've told you:
dy/dx = y/x --> y*dy = x*dx
• December 23rd 2008, 03:08 AM
GabrielKiefer
the problem is my teacher doesnt teach me anything so i dont know how to integrate or do any of this do you mind explaining further into the problem :)
• December 23rd 2008, 03:24 AM
Skalkaz
Ooops, I miscalculated:

dy / dx = y / x --> dy / y = dx / x
$\int x dx = ln(x) + C$
$\int y dy = ln(y)$
So $ln(y) = ln(x) + C$
so
$y = exp(ln(x)+C) = D*x$
D is constant.

controling:
dy / dx = D
and
y / x = D
• December 23rd 2008, 03:48 AM
mr fantastic
Quote:

Originally Posted by Skalkaz
Ooops, I miscalculated:

dy / dx = y / x --> dy / y = dx / x
$\int {\color{red}\frac{1}{x}} \, dx = ln(x) + C$
$\int {\color{red}\frac{1}{y}} \, dy = ln(y)$
So $ln(y) = ln(x) + C$
so
$y = exp(ln(x)+C) = D*x$
D is constant.

controling:
dy / dx = D
and
y / x = D

Please note the corrections (in red).