* A function y(t) satisfies the differential equation
a. What are the constant solutions of the equation ?
My answer : Solution :, is not depend t , therefore y are the constant solutions of the equation.
Right or wrong ?
b. For what values of y is y increasing ? --> Should be "For what values of t is y increasing " Right or worng ?
You'll notice that your equation can be written asOriginally Posted by butbi9x
* A function y(t) satisfies the differential equation
a. What are the constant solutions of the equation ?
My answer : Solution :
Right or wrong ?
b. For what values of y is y increasing ? --> Should be "For what values of t is y increasing " Right or worng ?
Now the question asks, for what constants (i.e. y = c) is this equation satisfied? Now between these constants eitherincreasing or
decreasing.
Sorry, but that makes no sense at all. You cannot simply write an equation with only y and deduce from the equation that y does not depend on t!* A function y(t) satisfies the differential equation
a. What are the constant solutions of the equation ?
My answer : Solution :
Right or wrong ?
Perhaps more importantly, you integrated the left side with respect to t,but integrated the right side with respect to y. You can't do that! If y is a constant then dy/dx= 0. Solve
. As danny arrigo pointed out, that can be easily factored.
No, you are not. y will be increasing when dy/dx> 0 and, since you can factor the right hand side, that will happen when an even number of those factors are negative.b. For what values of y is y increasing ? --> Should be "For what values of t is y increasing " Right or worng ?
can change sign only at y= 0, y= 1, y= 5. If y< 0, all 4 factors will be negative so the product is positive. If y is between 0 and 1, two factors will be negative so the product is still positive. If y is between 1 and 5, only y- 5 is negative so the product is negative. If y> 5, none of the factors is negative so the product is positive.
  |
LinkBack URL
About LinkBacks
