Differential Equations

(a) Let S be the set of solutions y(t) to the differential equation dy/dt = -y for t> 0. With addition and scalar multiplication of elements defined in the usual way, is S a vector space?

(b)Let T be the set of solution y(t) to the differential equation dy/dt = 1 - y for t > 0. With addition and scalar multiplication of elements defined in the usual way, is T a vector space?

  1. 👍 0
  2. 👎 0
  3. 👁 65
asked by Cam

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Consider the differential equation dy/dx=xy-y. Find d^2y/dx^2 in terms of x and y. Describe the region in the xy plane in which all solutions curves to the differential equation are concave down.

    asked by Michelle on May 1, 2014
  2. Differential Equations

    in this problem we consider an equation in differential form M dx+N dy=0 (2y-2xy^2)dx+(2x-2x^2y)dy=0 give implicit general solutions to the differential equation. F(x,y)=

    asked by Anonymous on February 15, 2016
  3. CountIblis, can i bother you

    Countiblis, i know that you might be busy do you mind if i ask you the following for help.Only if you can please. can you explain to me just one more thing so i can undestand it. Now i have an equation which is : 3x = 3x + 5 which

    asked by jasmine20 on January 3, 2007
  4. PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!!

    1) What are the equilibrium solutions to the differential equation and determine if it is stable or unstable with the initial condition y(-4)=1: 0.1(y+2)(4-y) 2) Use Euler's method with step size=0.5 and initial condition y(0)=3

    asked by Karen on December 8, 2014
  5. A Math Equation...Plz Help...

    |2x + 4| is always larger than or equal to zero. This means that the left hand side of the equation is always 6 or less, so there are no solutions. 6 - 3|2x + 4| = 12 So I just put NO Soution? No solutions, or if you have to write

    asked by Count Iblis on December 2, 2006
  6. Help with differential eqs problem???? (Calculus)

    Consider the differential equation dy/dt=y-t a) Determine whether the following functions are solutions to the given differential equation. y(t) = t + 1 + 2e^t y(t) = t + 1 y(t) = t + 2 b) When you weigh bananas in a scale at the

    asked by Stacey on November 30, 2014
  7. Math

    The maximum number of arbitrary constants is equal to a. Number of derivatives in the differential equation b. Degree of differential equation c. Order of differential equation e. None of the above I don't understand this, but my

    asked by Rin on September 13, 2014
  8. Math

    I need to solve this set of differential equations {y'+(t/2)1, y(0)=1} and then find the limiting value as t approaches infinity. I'm not sure where to start. I found the answer to the differential equation to be:

    asked by Emily on September 6, 2012
  9. math

    10. Sales of televisions grow at a rate proportional to the amount present (t is measured in days). (a)Set up a differential equation to model this problem. (b)Solve the differential equation if at t = 0, there are 20 televisions

    asked by dougal on May 31, 2007
  10. calculus-differential equation

    Consider the differential equation: (du/dt)=-u^2(t^3-t) a) Find the general solution to the above differential equation. (Write the answer in a form such that its numerator is 1 and its integration constant is C). u=? b) Find the

    asked by Jeff on February 5, 2008

More Similar Questions