Differential Equations

c) When a flexible cable of uniform density is suspended between two fixed points and hangs

of its own weight, the shape y = f(x) of the cable must satisfy a differential equation

d

2y

dx2

= k

s

1 +

dy

dx2

where k is a positive constant. Consider the cable shown in the Figure 1 below.

Figure 1: Cable hanging between two points.

i) Let z =

dy

dx in the differential equation. Solve the resulting first-order differential equa-

tion (in z), and then integrate to find y. [6]

ii) Determine the length of the cable.

of its own weight, the shape y = f(x) of the cable must satisfy a differential equation

d

2y

dx2

= k

s

1 +

dy

dx2

where k is a positive constant. Consider the cable shown in the Figure 1 below.

Figure 1: Cable hanging between two points.

i) Let z =

dy

dx in the differential equation. Solve the resulting first-order differential equa-

tion (in z), and then integrate to find y. [6]

ii) Determine the length of the cable.

Differential Equations

A series circuit contains a resistor with R = 40Ω, an inductor with L = 2 H, a capacitor with

0.0025 F, and a 12 − V battery. The initial charge is Q = 0.001 C and the initial current is

0. Using the method of undetermined coefficients, find the charge at time t A series circuit contains a resistor with R = 40Ω, an inductor with L = 2 H, a capacitor with

0.0025 F, and a 12 − V battery. The initial charge is Q = 0.001 C and the initial current is

0. Using the method of undetermined coefficients, find the charge at time t

0.0025 F, and a 12 − V battery. The initial charge is Q = 0.001 C and the initial current is

0. Using the method of undetermined coefficients, find the charge at time t A series circuit contains a resistor with R = 40Ω, an inductor with L = 2 H, a capacitor with

0.0025 F, and a 12 − V battery. The initial charge is Q = 0.001 C and the initial current is

0. Using the method of undetermined coefficients, find the charge at time t

Differential Equations

(y−(cosx)^2)dx+cosxdy=0

Differential Equations

Find the partial derivative of f(x,y,z)=x^2y+6z^3xy

Differential Equations

xy'=6y

Differential Equations

Solve

(D^2+DD'-6D'^2)z= ycosx

(D^2+DD'-6D'^2)z= ycosx

Differential Equations

Solve, by using the method of variation of parameter, the following differential equation

(D^2-3D+2)y = 1/(1+e^-x)

(D^2-3D+2)y = 1/(1+e^-x)

Differential Equations

cos^2y+sinxcosxcosy p=sinycos^2x using u=sinx and v=siny

Differential Equations

y^2logy=xpylogx+x^2p^2 by using logy=v,logx=u find G.S,S.S

Differential Equations

p^2(x^2-a^2)-2xyp+y^2+a^4=0 find G.S and S.S