Solve the boundary-value problem, if possible.

$$y’’-8y’+17y=0, y(0)=3, y(π)=2$$

Find the exact value of (a) $\sin ^ { - 1 } ( - 1 )\quad$ ( b ) $\cos ^ { - 1 } ( - 1 )$ (c) $tan ^ { - 1 } ( - 1 ) \quad$ (d) $\sec ^ { - 1 } ( 1 )$

Find the general solution to the given differential equation. s'' + 7s = 0

Give the number of vertices in the figure mentioned.

Identify the importance of Koch’s postulates.

Derive the stability condition (ignoring the boundary condition) for the three-dimensional heat equation if $\Delta x=\Delta y=\Delta z.$

What are Koch's postulates used for?

Solve the boundary-value problem, if possible.

$$y’’+4y=0, y(0)=5, y(π/4)=3$$

Find A + B.

$$A=\begin{bmatrix} 0 & 1&2\\ 1&-1& 0\\ 2&1& 1 \end{bmatrix}, \quad B=\begin{bmatrix} 0 & 1&-1\\ 2&1& 1\\ 0&1& 1 \end{bmatrix}$$

What is meant by the term Columbian Exchange?

Ciana wants to take out a $7,500 loan with a 5.3% APR. She can afford to pay$128 per month for loan payments. What would an increase of $20 to the monthly payment have do to the length of her loan?

Each of the differential equations (i)-(iv) represents the position of a 1 gram mass oscillating on the end of a damped spring. Pick the differential equation representing the system which answers the question. (i) s'' + s' + 4s = 0 (ii) s'' + 2s' + 5s = 0 (iii) s'' + 3s' + 3s = 0 (iv) s'' + 0.5s' + 2s = 0. In which system does the mass experience the frictional force of smallest magnitude for a given velocity?

Simplify. Give restrictions on the variables. $\frac{8}{5 m n}-\frac{2}{m}$

Solve the boundary-value problem, if possible.

$$y’’+4y’+20y=0, y(0)=1, y(π)=2$$