Quiz No.1 (final) period)
1. Use Laplace transforms to solve the differential equation: y ' ' + 4 y=20 e4 t with y(0)=3 and y’(0)=12
2. Determine the inverse laplace transform:
a) L
−1
{ 3 s 3 +s 2+ 12 s+2
( s−3)(s +1)3 }
b) L
−1
{
5 s 2−2 s−19
( s+ 3)(s−1)
2 }
n
2
3. Find the first four terms and the (n+1)st term of the series whose nth term is
n(n+1)
1 1 1 1
4. Find the nth for the series ,− , ,−
2 4 8 16
Quiz No.1 (final) period)
1. Use Laplace transforms to solve the differential equation: y ' ' + 4 y=20 e4 t with y(0)=3 and y’(0)=12
2. Determine the inverse laplace transform:
{ }
3 2
−1 3 s +s + 12 s+2
c) L
( s−3)(s +1)3
d) L
−1
{
5 s 2−2 s−19
( s+ 3)(s−1)2 }
n
2
3. Find the first four terms and the (n+1)st term of the series whose nth term is
n(n+1)
1 1 1 1
4. Find the nth for the series ,− , ,−
2 4 8 16
Quiz No.1 (final) period)
1. Use Laplace transforms to solve the differential equation: y ' ' + 4 y=20 e4 t with y(0)=3 and y’(0)=12
2. Determine the inverse laplace transform:
{ }
3 2
−1 3 s +s + 12 s+2
e) L 3
( s−3)(s +1)
f) L
−1
{
5 s 2−2 s−19
( s+ 3)(s−1)2 }
n
2
3. Find the first four terms and the (n+1)st term of the series whose nth term is
n(n+1)
1 1 1 1
4. Find the nth for the series ,− , ,−
2 4 8 16
Quiz No.1 (final) period)
1. Use Laplace transforms to solve the differential equation: y ' ' + 4 y=20 e4 t with y(0)=3 and y’(0)=12
2. Determine the inverse laplace transform:
g) L
−1
{ 3 s 3 +s 2+ 12 s+2
( s−3)(s +1)
3 }
{ }
2
−1 5 s −2 s−19
h) L
( s+ 3)(s−1)2
1. Use Laplace transforms to solve the differential equation: y ' ' + 4 y=20 e4 t with y(0)=3 and y’(0)=12
2. Determine the inverse laplace transform:
a) L
−1
{ 3 s 3 +s 2+ 12 s+2
( s−3)(s +1)3 }
b) L
−1
{
5 s 2−2 s−19
( s+ 3)(s−1)
2 }
n
2
3. Find the first four terms and the (n+1)st term of the series whose nth term is
n(n+1)
1 1 1 1
4. Find the nth for the series ,− , ,−
2 4 8 16
Quiz No.1 (final) period)
1. Use Laplace transforms to solve the differential equation: y ' ' + 4 y=20 e4 t with y(0)=3 and y’(0)=12
2. Determine the inverse laplace transform:
{ }
3 2
−1 3 s +s + 12 s+2
c) L
( s−3)(s +1)3
d) L
−1
{
5 s 2−2 s−19
( s+ 3)(s−1)2 }
n
2
3. Find the first four terms and the (n+1)st term of the series whose nth term is
n(n+1)
1 1 1 1
4. Find the nth for the series ,− , ,−
2 4 8 16
Quiz No.1 (final) period)
1. Use Laplace transforms to solve the differential equation: y ' ' + 4 y=20 e4 t with y(0)=3 and y’(0)=12
2. Determine the inverse laplace transform:
{ }
3 2
−1 3 s +s + 12 s+2
e) L 3
( s−3)(s +1)
f) L
−1
{
5 s 2−2 s−19
( s+ 3)(s−1)2 }
n
2
3. Find the first four terms and the (n+1)st term of the series whose nth term is
n(n+1)
1 1 1 1
4. Find the nth for the series ,− , ,−
2 4 8 16
Quiz No.1 (final) period)
1. Use Laplace transforms to solve the differential equation: y ' ' + 4 y=20 e4 t with y(0)=3 and y’(0)=12
2. Determine the inverse laplace transform:
g) L
−1
{ 3 s 3 +s 2+ 12 s+2
( s−3)(s +1)
3 }
{ }
2
−1 5 s −2 s−19
h) L
( s+ 3)(s−1)2
