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
Answer:
0
Step-by-step explanation: 2x+8=2x+6 --> 8=6
8 cant be equal to 6 so this equation is wrong and has no solution.
-7x^2 - 6x^2 + 3x + 5x - 5 + 2
-13x^2 + 8x - 3
You could subsitute g(x) for x in f(x) and if you get x as a result, then that is indeed the inverse
ex
if
f(x)=x-2
the inverse which is g(x) is
g(x)=x+2 because if you did
f(g(x)) then you would get
f(g(x))=(2+x)-2=2-2+x=x
