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quester [9]
3 years ago
7

What is the slope of the line through (-2,-6)(−2,−6)left parenthesis, minus, 2, comma, minus, 6, right parenthesis and (2,2)(2,2

)left parenthesis, 2, comma, 2, right parenthesis?
Mathematics
1 answer:
mojhsa [17]3 years ago
3 0

Answer:

y=2x-2

Step-by-step explanation:

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Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.
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\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}

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so the ODE is indeed exact and there is a solution of the form F(x,y)=C. We have

\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)

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