# Calculus

posted by .

Show that both functions y1=e^(-2x) and y2=xe^(-2x) are solutions to the differential equation y^''+4y^'+4y=0

• Calculus -

what's the troub;e? Just plug and chug

y1 = e^(-2x)
y1' = -2e^(-2x)
y1" = 4e^(-2x)

y"+4y'+4 = 0

y2 = xe^(-2x)
y2' = (1-2x) e^(-2x)
y2" = (4x-4) e^(-2x)

y"+4y'+4y = 0

## 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 AB

Verify if the given equations are solutions to the differential equation. dy/dt=k(y-a) i) y=1-ae^(kt) ii) y=a+Ce^(kt)
3. ### Differential Equations

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when …
4. ### Differential Equations

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when …
5. ### Differential Equations

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when …
6. ### 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.
7. ### 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 grocery …
8. ### 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 to …
9. ### 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)=
10. ### 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.

More Similar Questions

Post a New Question