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Download Module 7 FRQ Consider the differential equation given by $$\frac{dy
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Module 7 FRQ
Consider the differential equation given by $$\frac{dy}{dx}=\frac{x}{y}$$ .
(a) Sketch a slope field for the given equation on axes like the ones below.
Attach parts (a), (b), and (d) as an image file to your submission.
(b) Sketch a solution curve that passes through the point $$(0,1)$$ on your slope field.
Attach parts (a), (b), and (d) as an image file to your submission.
(c) Find the particular solution $$y=f(x)$$ to the differential equation with the initial condition
$$f(0)=1$$ .
(d) Sketch a solution curve that passes through the point $$(0,-1)$$ on your slope field.
Attach parts (a), (b), and (d) as an image file to your submission.
(e) Find the particular solution $$y=f(x)$$ to the differential equation with the initial condition
$$f(0)=-1$$ .
Answers:
(c) $$y=sqrt{x^2+1}$$
(e)$$ y=-sqrt{x^2+1}$$
