A tank with vertical sides has a square cross-section of area 4 ft squared. Water is leaving the tank through an orifice of area 5/3 inches squared. Water also flows into the tank at the rate of 100 cubic inches per second. Show that the water level approaches the value (25/24)^2 ft above the orifice.
Rate of discharge of volume through the orifice is cubic feet per second, where = size of orifice in square feet
By the chain rule, so
The problem right before this was the same except water was not being added at all, and that was an easily solvable differential equation. I am stuck on this, and when I got the answer from WolframAlpha it did not look encouraging that I was on the right track, so I think I have set up the problem incorrectly.