Differential Equations Answers

d^3y/dx^3-3 d^2y/dx^3+ 4 dy/dx -2y=e^x+cosx

d^3y/dx^3-3 d^2y/dx^3+ 4 dy/dx -2y=e^x+cosx

x3y3(2ydx+ xdy) = (5ydx+7xdy)

𝑦^1/2 𝑑𝑦/𝑑𝑥+𝑦3/2=1; 𝑦(0)=4

dx/1+y = dy/1+x = dz/z

4yzp+q+2y=0

(x^2+y^2)y prime =y^2

(x^2+y^2)y'=y^2

A particle of mass 5kg moves along x-axis under the influence of two forces;force of attraction to the origin which is numerically equal to 40 times the instantaneous distance from the origin and damping force is proportional to instantaneous speed; when the speed is 10m/s the damping is 200. Assuming that the particle from rest at a distance of 20cm from the origin then

a)Write the differential equations

b)Find the position at any given time t

c) Determine the amplitude, frequency and period of the damping oscillation.

(y+z)p+(z+x) =x+y