Differential Equations Answers

Solve . d²Bz(x)/dx²=Bz(x)/ some contant²
The z is in subscript and solve this equation.

if dx
dy
y e cos x sin x find ax 3 2 

If y = eax cos3x sin2x
find dy/dx.

Which of the following represent the solution of the differential equation d^2y/dx^2+4y=0

5tan2x+5cos2x
5sin2x+4cos2x
5sin2x−3cos2x
5sin^22x−3cos2x

Use the power series method to obtain one solution of the following ODE:
3 0
2
x y ′′ + y′ − xy

A mass of 2 kg is fixed to an end of a spring with spring constant k = 128 Nm−1
and the
system is placed inside a fluid. It is set into vibration from its equilibrium position with
an initial speed of 0.6 ms−1
. If the damping force due to the fluid is 40v(t) N where v is
the instantaneous speed of the mass, determine the position of the mass as a function of
time t.

A paratrooper weighing 80 kg jumps with zero velocity from an aeroplane at a height of
3000 m. The air resistance encountered by the paratrooper is 2 R t)( =15v t)( N where v(t)
is the velocity of the paratrooper at time t. Calculate the time required by the paratrooper
to land and the velocity at landing.

Solve the initial value problem:
2 2 ,0 )0( ,2 )0( 1
2
2
+ + y = y = y′ =
dx
dy
dx
d y

Solve the following ordinary differential equations:
i)

sin [ ] ( ) ln )(cos ) 0
1
ydx + x y + y dy =
x

1. If u = f(x,y) be a function of two independent variables x and y, then ∂u/∂y is equal to
a) lim△x→0f(x+△x,y)−f(x,y)△x
b) lim△y→0f(x,y+△y)−f(x,y)△y
c) limy→0f(x,y+△y)−f(x,y)△y
d) lim△y→0f(x+△x,y)−f(x,y)△x
2. Find the total differential of the function
u=x2y−3y

a)2x+(x2−3)dy
b) 2xydx+x2dy
c) 2xydx+(x2−3)dy
d) 2xydx+(x3−2)dy
3. The total differential du of a function u (x, y) = 0 is defined as

a) ∂u∂xdx+∂u∂xdy=0
b) ∂u∂xdy+∂u∂xdy=0
c) ∂u∂xdx+∂u∂ydx=0
d)∂u∂xdx+∂u∂ydy=0