First Order Differential Equation for Mixture Problem

[Outlaw747]

Homework Statement

$$\frac{dA}{dt}$$=$$\frac{5}{3}$$ - $$\frac{4A}{150+2.5t}$$ lb/min
so basically dA/dt = rate in - rate out

Homework Equations

This is basically a mixture problem. There is 10 gals/min going in and 4gals/min going out. Tank starts at 150/300 gallons with 1/4 lb/gal mixture. 5gal/min are coming in at 1/3 lb/gal mixture, other 5 is clean water.

The Attempt at a Solution

Derived this equation, tried to manipulate it algebraically, but not really sure how to proceed. Can't seem to separate the equation and integrate, all I really know is integration factors and substitution. Any help would be great. Thanks.

 

[Outlaw747]

Nevermind, got it using integration factor.