* 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 ?
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!
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.