MATH 20
QUIZ #8--SOLUTIONS

1.  Find the general solution of the separable differential equation y’ = 9x2y.

This differential equation is separable.

  
Type
   Differential Equation   
Solution
   Unlimited Growth   
y’ = ay
y = ceat
Limited Growth
y’ = a(M – y)
y = M(1 –e-at)
Logistic Growth
y’ = ay(M – y)
   (exponent is –aMt)   
2.  Find the solution to the differential equation and find the constants.  y’ = 2(100 – y), y(0) = 0
This represents limited growth with a = 2 and M = 100.  The solution is y = 100(1 – e-2t).

3.  Solve the first-order linear differential equation(x + 1)y’ + y = 2x.