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lisabon 2012 [21]
3 years ago
15

(10 pts) (a) (2 pts) What is the difference between an ordinary differential equation and an initial value problem? (b) (2 pts)

What is the difference between a particular solution and a general solution? (c) (3 pts) Given an example of a second-order linear ODE and a second-order nonlinear ODE that is not in the text, Chapter 1. (d) (3 pts) Give an example of a nonlinear 4th-order ordinary differential equation.
Mathematics
1 answer:
laiz [17]3 years ago
4 0

Answer:

Step-by-step explanation:

(A) The difference between an ordinary differential equation and an initial value problem is that an initial value problem is a differential equation which has condition(s) for optimization, such as a given value of the function at some point in the domain.

(B) The difference between a particular solution and a general solution to an equation is that a particular solution is any specific figure that can satisfy the equation while a general solution is a statement that comprises all particular solutions of the equation.

(C) Example of a second order linear ODE:

M(t)Y"(t) + N(t)Y'(t) + O(t)Y(t) = K(t)

The equation will be homogeneous if K(t)=0 and heterogeneous if K(t)\neq 0

Example of a second order nonlinear ODE:

Y=-3K(Y){2}

(D) Example of a nonlinear fourth order ODE:

K^4(x) - \beta f [x, k(x)] = 0

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IrinaK [193]

Answer:

63

Step-by-step explanation:

Based off of the question,we have a word problem that can be interpreted as the following. 6²+3³= ?

6² is the same as 6×6 which is equal to 36, In other words 6×6=36 or 6²=36

3³ is the same as 3×3×3 which is equal to 27, In other words 3×3×3=27 or

3³=27

Now with the product of each value in the word problem we can set up a statement as the following: 36+27= ?

Which when added together gives us the sum of 63, in other terms 36+27=63

concluding in our answer for the initial word problem. (6²+3³=63)

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$1689 invested for 4 years at 3% compounded annually ?
Ira Lisetskai [31]

The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901

The amount of money gained after an investment is compounded is given by:

A=P(1+\frac{r}{n} )^{nt}

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Given that P = $1689, t = 4, r = 3% = 0.03, n = 1, hence:

A=P(1+\frac{r}{n} )^{nt}\\\\A=1689(1+\frac{0.03}{1} )^{4*1}\\\\A=\$1901

The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901

Find out more at: brainly.com/question/14295570

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The volume of the slice is 129 in^3 and that of the remaining cake is 374. 4 in^3

<h3>How to determine the volume </h3>

Using the formula:

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h =height of the prism

Substitute values from the diagram into the formula

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