Question 1

Find the Laplace transform of $f(t)=\sin 4 t$ by direct integration.

Accepted Answer

$\frac{4}{s^{2}+16}$

Question 2

Use a table to find the Laplace transform of $f(t)=3 e^{2 t}-e^{-t}$.

Accepted Answer

$\frac{3}{s-2}-\frac{1}{s+1}$

Question 3

Use a table to find the Laplace transform of $f(t)=t e^{2 t}-t \cos 4 t$.

Accepted Answer

$\frac{1}{(s-2)^{2}}-\frac{s^{2}-16}{\left(s^{2}+16\right)^{2}}$

Question 4

Find the Laplace transform of $y^{\prime \prime}-4 y^{\prime}+4 y$, and substitute in the initial conditions, $y(0)=6, y^{\prime}(0)=0$.

Accepted Answer

The answer of Find the Laplace transform of \(y^{\prime \prime}-4...

Question 5

Find the Laplace transform of the function: $f(t)=\sin 5 t+2 t e^{t}$

Accepted Answer

The answer of Find the Laplace transform of the function:...

Question 6

Find the Laplace transform of the expression and substitute in the initial conditions: $2 y^{\prime \prime}+3 y^{\prime}+y$; $y^{\prime}(0,1)=2$

Accepted Answer

The answer of Find the Laplace transform of the expression...

Question 7

Find the Laplace transform of the function $f(t)=2 t-6$.

Accepted Answer

The answer of Find the Laplace transform of the function...

Question 8

Find the Laplace transform of the function $f(t)=t e^{3 t}+2 e^{7 t}$.

Accepted Answer

The answer of Find the Laplace transform of the function...

Question 9

Find the Laplace transform of $2 y^{\prime \prime}+5 y^{\prime}-3 y$ and substitute the initial condition $y^{\prime}(0,0)=0$.

Accepted Answer

The answer of Find the Laplace transform of \(2 y^{\prime...

Question 10

Find the Laplace transform of $y^{\prime \prime}+2 y^{\prime}+3 y$ and substitute the initial condition $y^{\prime}(0,6)=7$.

Accepted Answer

The answer of Find the Laplace transform of \(y^{\prime \prime}+2...

Question 11

Find the Laplace transform of $f(t)=5 t^{3}$ by direct integration.

Accepted Answer

The answer of Find the Laplace transform of $f(t)=5 t^{3}$...

Question 12

Find the Laplace transform of $4 y^{\prime}-7 y$, and substitute in the initial condition $y(0)=5$.

Accepted Answer

The answer of Find the Laplace transform of \(4 y^{\prime}-7...

Question 13

Use a table to find the Laplace transform of $f(t)=2 e^{-4 t} \cos 3 t$.

Accepted Answer

The answer of Use a table to find the Laplace...

Question 14

Find the Laplace transform of $f(t)=2 t^{2} e^{4 t}$.

Accepted Answer

The answer of Find the Laplace transform of \(f(t)=2 t^{2}...

Question 15

Find the Laplace transform of $2 y^{\prime \prime}-5 y^{\prime}-7 y$, and substitute in the initial condition $y^{\prime}(0,4)=3$.

Accepted Answer

The answer of Find the Laplace transform of \(2 y^{\prime...

Question 16

Find the Laplace transform of $f(t)=\sin 2 t+2 t \cos 2 t$.

Accepted Answer

The answer of Find the Laplace transform of \(f(t)=\sin 2...

Question 17

Find the Laplace transform of $4 y^{\prime \prime}-3 y$, and substitute in the initial condition $y^{\prime}(0,0)=5$.

Accepted Answer

The answer of Find the Laplace transform of \(4 y^{\prime...

Question 18

Find the inverse transform of $\frac{5}{S}$.

Accepted Answer

The answer of Find the inverse transform of $\frac{5}{S}$....

Question 19

Find the inverse transform of $\frac{1}{s^{2}+4 s+13}$.

Accepted Answer

The answer of Find the inverse transform of $\frac{1}{s^{2}+4 s+13}$....

Question 20

Find the inverse transform of $\frac{10s-3}{s(s+2)(s-3)}$.

Accepted Answer

The answer of Find the inverse transform of $\frac{10s-3}{s(s+2)(s-3)}$....

Quiz 36: Solving Differential Equations by the Laplace Transform and by Numerical Methods

Find the Laplace transform of $f(t)=\sin 4 t$ by direct integration.

Use a table to find the Laplace transform of $f(t)=3 e^{2 t}-e^{-t}$ .

Use a table to find the Laplace transform of $f(t)=t e^{2 t}-t \cos 4 t$ .

Find the Laplace transform of $y^{\prime \prime}-4 y^{\prime}+4 y$ , and substitute in the initial conditions, $y(0)=6, y^{\prime}(0)=0$ .

Find the Laplace transform of the function: $f(t)=\sin 5 t+2 t e^{t}$

Find the Laplace transform of the expression and substitute in the initial conditions: $2 y^{\prime \prime}+3 y^{\prime}+y$ ; $y^{\prime}(0,1)=2$

Find the Laplace transform of the function $f(t)=2 t-6$ .

Find the Laplace transform of the function $f(t)=t e^{3 t}+2 e^{7 t}$ .

Find the Laplace transform of $2 y^{\prime \prime}+5 y^{\prime}-3 y$ and substitute the initial condition $y^{\prime}(0,0)=0$ .

Find the Laplace transform of $y^{\prime \prime}+2 y^{\prime}+3 y$ and substitute the initial condition $y^{\prime}(0,6)=7$ .

Find the Laplace transform of $f(t)=5 t^{3}$ by direct integration.

Find the Laplace transform of $4 y^{\prime}-7 y$ , and substitute in the initial condition $y(0)=5$ .

Use a table to find the Laplace transform of $f(t)=2 e^{-4 t} \cos 3 t$ .

Find the Laplace transform of $f(t)=2 t^{2} e^{4 t}$ .

Find the Laplace transform of $2 y^{\prime \prime}-5 y^{\prime}-7 y$ , and substitute in the initial condition $y^{\prime}(0,4)=3$ .

Find the Laplace transform of $f(t)=\sin 2 t+2 t \cos 2 t$ .

Find the Laplace transform of $4 y^{\prime \prime}-3 y$ , and substitute in the initial condition $y^{\prime}(0,0)=5$ .

Find the inverse transform of $\frac{5}{S}$ .

Find the inverse transform of $\frac{1}{s^{2}+4 s+13}$ .

Find the inverse transform of $\frac{10s-3}{s(s+2)(s-3)}$ .

Quiz 36: Solving Differential Equations by the Laplace Transform and by Numerical Methods

Find the Laplace transform of f(t)=sin⁡4tf(t)=\sin 4 tf(t)=sin4t by direct integration.

Use a table to find the Laplace transform of f(t)=3e2t−e−tf(t)=3 e^{2 t}-e^{-t}f(t)=3e2t−e−t .

Use a table to find the Laplace transform of f(t)=te2t−tcos⁡4tf(t)=t e^{2 t}-t \cos 4 tf(t)=te2t−tcos4t .

Find the Laplace transform of y′′−4y′+4yy^{\prime \prime}-4 y^{\prime}+4 yy′′−4y′+4y , and substitute in the initial conditions, y(0)=6,y′(0)=0y(0)=6, y^{\prime}(0)=0y(0)=6,y′(0)=0 .

Find the Laplace transform of the function: f(t)=sin⁡5t+2tetf(t)=\sin 5 t+2 t e^{t}f(t)=sin5t+2tet

Find the Laplace transform of the expression and substitute in the initial conditions: 2y′′+3y′+y2 y^{\prime \prime}+3 y^{\prime}+y2y′′+3y′+y ; y′(0,1)=2y^{\prime}(0,1)=2y′(0,1)=2

Find the Laplace transform of the function f(t)=2t−6f(t)=2 t-6f(t)=2t−6 .

Find the Laplace transform of the function f(t)=te3t+2e7tf(t)=t e^{3 t}+2 e^{7 t}f(t)=te3t+2e7t .

Find the Laplace transform of 2y′′+5y′−3y2 y^{\prime \prime}+5 y^{\prime}-3 y2y′′+5y′−3y and substitute the initial condition y′(0,0)=0y^{\prime}(0,0)=0y′(0,0)=0 .

Find the Laplace transform of y′′+2y′+3yy^{\prime \prime}+2 y^{\prime}+3 yy′′+2y′+3y and substitute the initial condition y′(0,6)=7y^{\prime}(0,6)=7y′(0,6)=7 .

Find the Laplace transform of f(t)=5t3f(t)=5 t^{3}f(t)=5t3 by direct integration.

Find the Laplace transform of 4y′−7y4 y^{\prime}-7 y4y′−7y , and substitute in the initial condition y(0)=5y(0)=5y(0)=5 .

Use a table to find the Laplace transform of f(t)=2e−4tcos⁡3tf(t)=2 e^{-4 t} \cos 3 tf(t)=2e−4tcos3t .

Find the Laplace transform of f(t)=2t2e4tf(t)=2 t^{2} e^{4 t}f(t)=2t2e4t .

Find the Laplace transform of 2y′′−5y′−7y2 y^{\prime \prime}-5 y^{\prime}-7 y2y′′−5y′−7y , and substitute in the initial condition y′(0,4)=3y^{\prime}(0,4)=3y′(0,4)=3 .

Find the Laplace transform of f(t)=sin⁡2t+2tcos⁡2tf(t)=\sin 2 t+2 t \cos 2 tf(t)=sin2t+2tcos2t .

Find the Laplace transform of 4y′′−3y4 y^{\prime \prime}-3 y4y′′−3y , and substitute in the initial condition y′(0,0)=5y^{\prime}(0,0)=5y′(0,0)=5 .

Find the inverse transform of 5S\frac{5}{S}S5​ .

Find the inverse transform of 1s2+4s+13\frac{1}{s^{2}+4 s+13}s2+4s+131​ .

Find the inverse transform of 10s−3s(s+2)(s−3)\frac{10s-3}{s(s+2)(s-3)}s(s+2)(s−3)10s−3​ .

Find the Laplace transform of $f(t)=\sin 4 t$ by direct integration.

Use a table to find the Laplace transform of $f(t)=3 e^{2 t}-e^{-t}$ .

Use a table to find the Laplace transform of $f(t)=t e^{2 t}-t \cos 4 t$ .

Find the Laplace transform of $y^{\prime \prime}-4 y^{\prime}+4 y$ , and substitute in the initial conditions, $y(0)=6, y^{\prime}(0)=0$ .

Find the Laplace transform of the function: $f(t)=\sin 5 t+2 t e^{t}$

Find the Laplace transform of the expression and substitute in the initial conditions: $2 y^{\prime \prime}+3 y^{\prime}+y$ ; $y^{\prime}(0,1)=2$

Find the Laplace transform of the function $f(t)=2 t-6$ .

Find the Laplace transform of the function $f(t)=t e^{3 t}+2 e^{7 t}$ .

Find the Laplace transform of $2 y^{\prime \prime}+5 y^{\prime}-3 y$ and substitute the initial condition $y^{\prime}(0,0)=0$ .

Find the Laplace transform of $y^{\prime \prime}+2 y^{\prime}+3 y$ and substitute the initial condition $y^{\prime}(0,6)=7$ .

Find the Laplace transform of $f(t)=5 t^{3}$ by direct integration.

Find the Laplace transform of $4 y^{\prime}-7 y$ , and substitute in the initial condition $y(0)=5$ .

Use a table to find the Laplace transform of $f(t)=2 e^{-4 t} \cos 3 t$ .

Find the Laplace transform of $f(t)=2 t^{2} e^{4 t}$ .

Find the Laplace transform of $2 y^{\prime \prime}-5 y^{\prime}-7 y$ , and substitute in the initial condition $y^{\prime}(0,4)=3$ .

Find the Laplace transform of $f(t)=\sin 2 t+2 t \cos 2 t$ .

Find the Laplace transform of $4 y^{\prime \prime}-3 y$ , and substitute in the initial condition $y^{\prime}(0,0)=5$ .

Find the inverse transform of $\frac{5}{S}$ .

Find the inverse transform of $\frac{1}{s^{2}+4 s+13}$ .

Find the inverse transform of $\frac{10s-3}{s(s+2)(s-3)}$ .