Differential Equations Answers

A vibrational system consisting of mass 1/10 kg is attached to a spring (spring constant= 4kg/m). The mass is released from rest 1m below the equilibrium position. the motion is damped (damping constant=1.2) and is being driven by an external force 5sin4t, beginning at t=0. Write the governing equations of the system and intrepet the type of motion. Hence find the position of mass at time t.

Using elimination of arbitrary constant
y^2 (a-x) = x^2 (a+x)

3x²y²dx + 4(x³y -3) dy = 0

(y^2+z^2)p - xyq + xz = 0

(x^2-x-2)y’+3xy=x^2-4x+4

2y'+3y=e2x

Solve the following system of ODE:

x' - y - y' = -e^t

Classify the equation zxx + xzyy = 0 for x > 0 and reduce it to canonical form.

1. y'-2y=y^2 ;y=3 when x=0
2. (y')^2=(1-y^2)/(1-x^2); y=1/2 when x=1
3. x(e^y)dy+((x^2)+1dx)/y=0