# Math Help - Another First-Order Separable ODE

1. ## Another First-Order Separable ODE

Find the solution of the differential equation that satisfies the given initial condition.

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

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

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

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

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 $\sin(\frac{\pi}{2})$, but it rejected that solution.

Does anybody see what they want me to enter here? Thanks.

2. ## 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

3. ## re: Another First-Order Separable ODE

That was it. Thanks. I couldn't see where they were going, but now I do.