Answer:
Verified


Step-by-step explanation:
Question:-
- We are given the following non-homogeneous ODE as follows:

- A general solution to the above ODE is also given as:

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.
Solution:-
- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.
- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

- Therefore, the complete solution to the given ODE can be expressed as:

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

- Therefore, the complete solution to the given ODE can be expressed as:

Answer:
n= 18 over 5
Step-by-step explanation:
Answer:
x-y=4
and
x+y=32 is <u>your</u><u> </u><u>equation</u>
<u>d</u><u>i</u><u>f</u><u>f</u><u>e</u><u>r</u><u>e</u><u>n</u><u>c</u><u>e</u><u> </u><u>o</u><u>f</u><u> </u><u>t</u><u>w</u><u>o</u><u> </u><u>n</u><u>u</u><u>m</u><u>b</u><u>e</u><u>r</u><u> </u><u>=</u><u>x-y</u><u> </u><u>is</u><u> </u><u>equal</u><u> </u><u>to</u><u> </u><u>4</u>
<u>s</u><u>u</u><u>m</u><u> </u><u>o</u><u>f</u><u> </u><u>t</u><u>w</u><u>o</u><u> </u><u>n</u><u>u</u><u>m</u><u>b</u><u>e</u><u>r</u><u>=</u><u>x</u><u>+</u><u>y</u><u> </u><u>i</u><u>s</u><u> </u><u>e</u><u>q</u><u>u</u><u>a</u><u>l</u><u> </u><u>t</u><u>o</u><u> </u><u>3</u><u>2</u>
<u>x</u><u>-</u><u>y</u><u>=</u><u>4</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>(</u><u>1</u><u>)</u>
<u>x</u><u>+</u><u>y</u><u>=</u><u>3</u><u>2</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>(</u><u>2</u><u>)</u>
<u>a</u><u>d</u><u>d</u><u>i</u><u>n</u><u>g</u><u> </u><u>equation</u><u> </u><u>1</u><u> </u><u>a</u><u>n</u><u>d</u><u> </u><u>2</u>
<u>x</u><u>-</u><u>y</u><u> </u><u>+</u><u>x</u><u>+</u><u>y</u><u>=</u><u>4</u><u>+</u><u>3</u><u>2</u>
<u>2</u><u>x</u><u>=</u><u>3</u><u>6</u>
<u>x</u><u>=</u><u>3</u><u>6</u><u>/</u><u>2</u><u>=</u><u>1</u><u>6</u><u>a</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u>
<u>s</u><u>u</u><u>b</u><u>s</u><u>t</u><u>i</u><u>t</u><u>u</u><u>t</u><u>i</u><u>n</u><u>g</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>y</u><u> </u><u>in</u><u> </u><u>equation</u><u> </u><u>1</u>
<u>1</u><u>6</u><u>-</u><u>y</u><u>=</u><u>4</u>
<u>1</u><u>6</u><u>-</u><u>4</u><u>=</u><u>y</u>
<u>y</u><u>=</u><u>1</u><u>2</u><u> </u><u>a</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u>
2800 x 0.07 = 196
2800 + 196 = 2996
Total paid = $2996
Answer:115 miles/hour
Step-by-step explanation: one mile equals to 5280 feet, so 607200 divided into 5280 is 115 and as your timing don’t change you can convert only the distance