Unformatted text preview: dx dt = ( x 2 + 1) 1et , x (1) = 1 (Note: I “ﬁxed” the initial condition to make it nicer than the original value of π/ 4 that I had posted.). 4. Use the substitution v = y/x to solve the differential equation y = x + y xy • First calculate y in terms of x , v and v . • Substitute into the differential equation and replace all expressions involving y with expressions in v and x . • Solve the resulting differential equation for v (implicit form is ok). • Rewrite your solution to give an implicit solution for y . 5. A tank that can hold 1000L of water starts with 500L of salt water with concentration 0.1kg/L. We pump brine with a concentration of 1kg/L (of salt) into the tank at a rate of 50L/hour. Assume that the liquid is always well mixed. (a) What will the concentration of salt be in the tank when the tank ﬁrst overﬂows? (b) What will the concentration of salt in the tank be 15 hours after it overﬂows?...
View
Full Document
 Spring '08
 INDIK
 Math, Differential Equations, Equations, Boundary value problem

Click to edit the document details