# Another First-Order Separable ODE

• Sep 29th 2011, 06:46 PM
joatmon
Another First-Order Separable ODE
Find the solution of the differential equation that satisfies the given initial condition. http://www.webassign.net/cgi-perl/sy...0%29%20%3D%201

$\displaystyle (5+y^2)dy = y \cos(x) dx$

$\displaystyle \frac{(5+y^2)}{y}dy = \cos(x) dx$

$\displaystyle \int \frac{5}{y}dy + \int y dy = \int \cos(x) dx$

$\displaystyle 5 \ln|y| + \frac{1}{2}y^2 = \sin(x) + C$

The problem (this is on a web site) has the same left side of the equation that I have arrived at. It wants me to enter the right side of the equation. I tried entering $\displaystyle \sin(\frac{\pi}{2})$, but it rejected that solution.

Does anybody see what they want me to enter here? Thanks.
• Sep 29th 2011, 06:53 PM
pickslides
re: Another First-Order Separable ODE
Looks o.k to me, do you need to solve for C maybe?

Use x=0, y=1 gives C= 1/2
• Sep 29th 2011, 07:00 PM
joatmon
re: Another First-Order Separable ODE
That was it. Thanks. I couldn't see where they were going, but now I do.