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Masteriza [31]
3 years ago
10

Obtain the general solution to the equation. (x^2+10) + xy = 4x=0 The general solution is y(x) = ignoring lost solutions, if any

.
Mathematics
1 answer:
alukav5142 [94]3 years ago
6 0

Answer:

y(x)=4+\frac{C}{\sqrt{x^2+10}}

Step-by-step explanation:

We are given that a differential equation

(x^2+10)y'+xy-4x=0

We have to find the general solution of given differential equation

y'+\frac{x}{x^2+10}y-\frac{4x}{x^2+10}=0

y'+\frac{x}{x^2+10}y=4\frac{x}{x^2+10}

Compare with

y'+P(x) y=Q(x)

We get

P(x)=\frac{x}{x^2+10}

Q(x)=\frac{4x}{x^2+10}

I.F=e^{\int\frac{x}{x^2+10} dx}=e^{\frac{1}{2}ln(x^2+10)}

e^{ln\sqrt(x^2+10)}=\sqrt{x^2+10}

y\cdot \sqrt{x^2+10}=\int \frac{4x}{x^2+10}\times \sqrt{x^2+10} dx+C

y\cdot \sqrt{x^2+10}=\int \frac{4x}{\sqrt{x^2+10}}+C

y\cdot \sqrt{x^2+10}=4\sqrt{x^2+10}+C

y(x)=4+\frac{C}{\sqrt{x^2+10}}

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The point (4,7) is on the graph of y=x^2+c. what is the value of c?
slamgirl [31]
Point is (4,7)
So y = 7 = 4^2 + c
c = 7 - 16
c = -9
7 0
3 years ago
Hazel knits 5 centimeters of scarf eachnight. After 5 nights of knitting, how manycentimeters of scarf will Hazel have knit into
natta225 [31]

Answer:

Hazel will have knitted 25 centimeters of the scarf

SOLUTION

Problem Statement

We are told Hazel knits 5 centimeters of scarf every night for 5 nights. We are required to find the length of the scarf Hazel will have knitted after 5 nights.

Solution

We are told Hazel makes 5 centimeters of scarf every night. Thus, for each night up till 5 nights, we just need to add the length of scarf Hazel has made.

Let us count for each night.

Night 1:

Hazel makes 5 centimeters of the scarf.

Night 2:

Hazel makes extra 5 centimeters, which means she has made:

\begin{gathered} (5+5)\text{centimeters} \\ =10\text{ centimeters} \end{gathered}

Night 3:

Hazel makes extra 5 centimeters, which means she has made:

\begin{gathered} (10+5)\text{centimeters} \\ =15\text{ centimeters} \end{gathered}

NIght 4:

Hazel makes extra 5 centimeters, which means she has made:

\begin{gathered} (15+5)\text{centimeters} \\ =20\text{ centimeters} \end{gathered}

NIght 5:

Hazel makes extra 5 centimeters, which means she has made:

\begin{gathered} (20+5)\text{centimeters} \\ =25\text{ centimeters} \end{gathered}

Final Answer

Thus, Hazel will have knitted 25 centimeters of the scarf

5 0
10 months ago
What is the coefficient in the following expression?
Y_Kistochka [10]
The coefficient is 4 because it is placed before x.
7 0
2 years ago
Someone answer quick please for brainliest !
Rina8888 [55]

Answer:

The equation of the line is

y =  -  \frac{1}{2} x +  \frac{5}{2}

Step-by-step explanation:

Equation of a line is

y = mx + c

Where m is the slope

c is the y intercept

y = 2x + 3

Comparing with the above formula

m is 2

Since the lines are perpendicular the slope of the other line is the negative inverse of the original line .

That's

m = - 1/2

Equation of the line using point (1,2) and slope - 1/2 is

y - 2 = -1/2(x - 1)

y - 2 = -1/2x + 1/2

y = -1/2x + 1/2 + 2

The final answer is

y =   - \frac{1}{2} x +  \frac{5}{2}

Hope this helps you.

8 0
3 years ago
Helppp! Is Figure A’B’C’D’ a reflection of Figure ABCD? Explain. *
Korolek [52]
Yes. It would be a reflection over the line.
8 0
3 years ago
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