We write the equation in terms of dy/dx,
<span>y'(x)=sqrt (2y(x)+18)</span>
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9))
Separating the variables in the equation, we will have:
<span>1/sqrt(y + 9) dy= sqrt(2) dx </span>
Integrating both sides, we will obtain
<span>2sqrt(y+9) = x(sqrt(2)) + c </span>
<span>where c is a constant and can be determined by using the boundary condition given </span>
<span>y(5)=9 : x = 5, y = 9
</span><span>sqrt(9+9) = 5/sqrt(2) + C </span>
<span>C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2</span>
Substituting to the original equation,
sqrt(y+9) = x/sqrt(2) + sqrt(2) / 2
<span>sqrt(y+9) = (2x + 2) / 2sqrt(2)
</span>
Squaring both sides, we will obtain,
<span>y + 9 = ((2x+2)^2) / 8</span>
y = ((2x+2)^2) / 8 - 9
I believe that the answer is 1/5 but i am not entirely sure
Answer:
Enter a problem...
Algebra Examples
Popular Problems Algebra Solve by Substitution 3x-4y=9 , -3x+2y=9
3
x
−
4
y
=
9
,
−
3
x
+
2
y
=
9
Solve for
x
in the first equation.
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x
=
3
+
4
y
3
−
3
x
+
2
y
=
9
Replace all occurrences of
x
in
−
3
x
+
2
y
=
9
with
3
+
4
y
3
.
x
=
3
+
4
y
3
−
3
(
3
+
4
y
3
)
+
2
y
=
9
Simplify
−
3
(
3
+
4
y
3
)
+
2
y
.
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x
=
3
+
4
y
3
−
9
−
2
y
=
9
Solve for
y
in the second equation.
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Move all terms not containing
y
to the right side of the equation.
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x
=
3
+
4
y
3
−
2
y
=
18
Divide each term by
−
2
and simplify.
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x
=
3
+
4
y
3
y
=
−
9
Replace all occurrences of
y
in
x
=
3
+
4
y
3
with
−
9
.
x
=
3
+
4
(
−
9
)
3
y
=
−
9
Simplify
3
+
4
(
−
9
)
3
.
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x
=
−
9
y
=
−
9
The solution to the system of equations can be represented as a point.
(
−
9
,
−
9
)
The result can be shown in multiple forms.
Point Form:
(
−
9
,
−
9
)
Equation Form:
x
=
−
9
,
y
=
−
9
image of graph
Answer: The one on the right. Each side is multiplied by 6, therefore they are similar.
