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xenn [34]
3 years ago
6

Solve the differential equations dy/dx=((xy^2)+x)/y

Mathematics
1 answer:
arsen [322]3 years ago
7 0

\displaystyle \dfrac{dy}{dx}=\dfrac{xy^2+x}{y}\\ \dfrac{dy}{dx}=\dfrac{x(y^2+1)}{y}\\ \dfrac{y}{y^2+1}\, dy=x\, dx\\ \int \dfrac{y}{y^2+1}\, dy=\int x\, dx\\ \dfrac{\ln (y^2+1)}{2}=\dfrac{x^2}{2}+C\\ \ln(y^2+1)=x^2+C\\ y^2+1=e^{x^2+C}\\ y^2=e^{x^2+C}-1\\ y=\sqrt{e^{x^2+C}-1} \vee y=-\sqrt{e^{x^2+C}-1}\\ \boxed{y=\sqrt{Ce^{x^2}-1} \vee y=-\sqrt{Ce^{x^2}-1}}\\

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The rule T 5, -0.5° Ro, 1800(x, ) is applied to FGH to
Yuki888 [10]

Answer:

Step-by-step explanation:

Given rule for the multiple translations is,

T_{5,-0.5}.R_{0.180^{\circ}}(x,y)

Apply the rule R_{0,180^{\circ}} first.

(x, y) → (-x, -y)

This rule illustrates a rotation of the triangle FGH by 180° about the origin,

Vertices of ΔFGH are,

F → (1, 1)

G → (4, 5)

H → (5, 1)

After rotation vertices of the image triangle are,

F' → (-1, -1)

G' → (-4, -5)

H' → (-5, -1)

Further apply the rule,

T_{5,-0.5}

(x, y) → (x + 5, y - 0.5)

By this rule of translation,

F'(-1, -1) → F"{(-1 + 5), (-1 - 0.5)}

            → F"(4, -1.5)

G'(-4, -5) → G"[(-4 + 5), (-5 - 0.5)]

              → G"(1, -5.5)

H'(-5, -1) → H"[(-5 + 5), (-1 -0.5)]

             → H"(0, -1.5)

8 0
2 years ago
Tevon,leah,and beth are playing a computer game. Trevon scored -8. Beth's score was 3/4 of trever's score, and leah's score was
faust18 [17]

Answer:

Trevon scored -8.

Beth's score was 3/4 of trever's score = -8 *3/4 = -6

leah's score was 1/4 of beth's score. = -6 *1/4 = -1.5

Leah's score was -1.5


8 0
3 years ago
When CA= 3x-1 and SR=5x+4, what is CA?
avanturin [10]

Answer:

CA=17

Step-by-step explanation:

From given picture we see that A and C are the mid points of sides QR and QS respectively.

We know that line joining mid points of the two sides of triangle is always half of the length of the third side.

So that means:

2*CA=SR

2(3x-1)=5x+4

6x-2=5x+4

6x-5x=4+2

x=6

plug value of x into CA=3x-1

CA=3*6-1=18-1=17

Hence final answer is CA=17

8 0
3 years ago
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Jlenok [28]
1.3 meters below the surface of the water
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2 years ago
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lawyer [7]

Answer:

1/6

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Hope this helps!

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