AB Calculus

posted by .

So I'm supposed to verify the solution of the differential equation. The solution is y=e^(-x). The differential equation is 3y' + 4y = e^(-x). What is the problem asking me to do here?

  • AB Calculus -

    plug in y to see whether it satisfies the differential equation

    y = e^(-x)
    y' = -e^(-x)

    3y' + 4y = -3e^(-x) + 4e^(-x) = e^-x

    so, it does satisfy it.

  • AB Calculus -

    Oh, okay. I get it now. Thanks!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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=?
  2. calculus differential equation

    Find in implicit form the general solution of differential equation dy/dx=2(e^x-e^-x)/y^2(e^x+e^-x)^4 with (y>0). I know this requires a seperation of variables but I beyond that I am confused by how.Thanks.
  3. calculus

    verify that y=c/x^2 is a general solution of the differential equation y'+(2/x) y=0-6y=0 then find a particular solution of the differential equation that satisfies the side condition y(1)=2
  4. Calculus

    Which of the following is a separable, first-order differential equation?
  5. Physics

    Verify that the formula u(t)=Acos(ωo*t+Φ) is a solution to the differential equation for the mass on a spring, by plugging this expression for u(t) directly into the differential equation: d^2u/dt^2+ωo^2*u=0.
  6. Calculus!!

    Consider the differential equation given by dy/dx = xy/2. A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to f(0)?
  7. ordinary differential equation

    consider the differential equation d^3x/dt^3 - 9(d^2x/dt^2)+ 27(dx/dt) -27x = c0s t +sin t + te^(3t) a) show that characteristic equation of the differential equation is (m-3)^3 =0 (b) Hence, find the general solution of the equation.
  8. Calculus

    Consider the differential equation dy/dx = x^4(y - 2). Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 0. Is this y=e^(x^5/5)+4?
  9. Calculus

    Consider the differential equation dy/dx = x^2(y - 1). Find the particular solution to this differential equation with initial condition f(0) = 3. I got y = e^(x^3/3) + 2.
  10. Math (Calc) (Differential Equation Solution)

    Some of the curves corresponding to different values of C in the general solution of the differential equation are shown in the graph. Find the particular solution that passes through the point (0, 2). y(x^2+y) = C 2xy + (x^2+2y)y' …

More Similar Questions