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Differential Equations
if dx
dy
y e cos x sin x find ax 3 2
dy
y e cos x sin x find ax 3 2
Differential Equations
If y = eax cos3x sin2x
find dy/dx.
find dy/dx.
Differential Equations
Obtain the Fourier series expansion for the following periodic function which has a period of
2π:
π ≤ ≤ π
+ π − π ≤ ≤
=
x
x x
f x
for 0
for 0
2π:
π ≤ ≤ π
+ π − π ≤ ≤
=
x
x x
f x
for 0
for 0
Differential Equations
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
5tan2x+5cos2x
5sin2x+4cos2x
5sin2x−3cos2x
5sin^22x−3cos2x
Differential Equations
Use the power series method to obtain one solution of the following ODE:
3 0
2
x y ′′ + y′ − xy
3 0
2
x y ′′ + y′ − xy
Differential Equations
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.
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.
Differential Equations
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.
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.
Differential Equations
Solve the initial value problem:
2 2 ,0 )0( ,2 )0( 1
2
2
+ + y = y = y′ =
dx
dy
dx
d y
2 2 ,0 )0( ,2 )0( 1
2
2
+ + y = y = y′ =
dx
dy
dx
d y
Differential Equations
y e
dx
dy
dx
d y 2
2
2
+ −12 = 4
dx
dy
dx
d y 2
2
2
+ −12 = 4
Differential Equations
Solve the following ordinary differential equations:
i)
sin [ ] ( ) ln )(cos ) 0
1
ydx + x y + y dy =
x
i)
sin [ ] ( ) ln )(cos ) 0
1
ydx + x y + y dy =
x
