Question 1

For the problems below, solve each differential equation.
-  $y^{\prime \prime}+4 y^{\prime}-21 y=0$

Accepted Answer

The answer of For the problems below, solve each differential...

Question 2

A spring is stretched $8 \mathrm{in}$. by a weight of $25 \mathrm{lb}$. A damping force exerts a force of $6 \mathrm{lb}$ for a velocity of $5 \mathrm{in}$./s. If the weight is displaced from the rest position and then released, find the general equation of motion.

Accepted Answer

The answer of A spring is stretched $8 \mathrm{in}$. by...

Question 3

For the problems below, solve each differential equation.
-  $y^{\prime \prime}-22 y^{\prime}+121 y=0$

Accepted Answer

The answer of For the problems below, solve each differential...

Question 4

Find the general solution of the differential equation $y^{\prime \prime}+5 y^{\prime}+6 y=0$.

Accepted Answer

A)  $y=k_{1} e^{-5 x}+k_{2} e^{-x}$ 
B)  $y=k_{1} e^{-3 x}+k_{2} e^{-2 x}$ 
C)  $y=k_{1} e^{3 x}+k_{2} e^{2 x}$ 
D)  $y=k_{1} e^{5 x}+k_{2} e^{x}$ 
A)  $y=k_{1} e^{-5 x}+k_{2} e^{-x}$ 
B)  $y=k_{1} e^{-3 x}+k_{2} e^{-2 x}$ 
C)  $y=k_{1} e^{3 x}+k_{2} e^{2 x}$ 
D)  $y=k_{1} e^{5 x}+k_{2} e^{x}$

Question 5

Using a table of Laplace transforms, find the Laplace transform of $f(t)=t e^{-3 t}$.

Accepted Answer

A)  $\frac{1}{(s-3)^{2}}$ 
B)  $\frac{\mathrm{s}}{(\mathrm{s}+3)^{2}}$ 
C)  $\frac{s^{2}}{s-3}$ 
D)  $\frac{1}{(s+3)^{2}}$ 
A)  $\frac{1}{(s-3)^{2}}$ 
B)  $\frac{\mathrm{s}}{(\mathrm{s}+3)^{2}}$ 
C)  $\frac{s^{2}}{s-3}$ 
D)  $\frac{1}{(s+3)^{2}}$

For the problems below, solve each differential equation. - $y^{\prime \prime}+4 y^{\prime}-21 y=0$

A spring is stretched $8 \mathrm{in}$ . by a weight of $25 \mathrm{lb}$ . A damping force exerts a force of $6 \mathrm{lb}$ for a velocity of $5 \mathrm{in}$ ./s. If the weight is displaced from the rest position and then released, find the general equation of motion.

For the problems below, solve each differential equation. - $y^{\prime \prime}-22 y^{\prime}+121 y=0$

Find the general solution of the differential equation $y^{\prime \prime}+5 y^{\prime}+6 y=0$ .

Using a table of Laplace transforms, find the Laplace transform of $f(t)=t e^{-3 t}$ .

Analytic Geometry

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

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Exam 12: Second-Order Differential Equations

For the problems below, solve each differential equation. - y′′+4y′−21y=0y^{\prime \prime}+4 y^{\prime}-21 y=0y′′+4y′−21y=0

A spring is stretched 8in8 \mathrm{in}8in . by a weight of 25lb25 \mathrm{lb}25lb . A damping force exerts a force of 6lb6 \mathrm{lb}6lb for a velocity of 5in5 \mathrm{in}5in ./s. If the weight is displaced from the rest position and then released, find the general equation of motion.

For the problems below, solve each differential equation. - y′′−22y′+121y=0y^{\prime \prime}-22 y^{\prime}+121 y=0y′′−22y′+121y=0

Find the general solution of the differential equation y′′+5y′+6y=0y^{\prime \prime}+5 y^{\prime}+6 y=0y′′+5y′+6y=0 .

Using a table of Laplace transforms, find the Laplace transform of f(t)=te−3tf(t)=t e^{-3 t}f(t)=te−3t .