Part (a) dy dx = 1+y x dy dx = 1+1 1 m = 2

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Presentation transcript:

Part (a) dy dx = 1+y x dy dx = 1+1 1 m = 2 Keep in mind that dy/dx is the SLOPE! We simply need to substitute x and y into the differential equation and represent each answer as a slope on the graph.

Part (a) dy dx = 1+y x dy dx = 1+0 -2 m = -1/2 Repeating this process for the remaining six points gives us the following slope field…

Separate the variables Part (b) dy dx = 1+y x Cross multiply = (1+y) dx x dy Separate the variables Integrate both sides = x-1 dx (1+y)-1 dy = ln x + C ln 1+y

Plug in the initial condition Part (b) Plug in the initial condition = ln -1 + C ln 1+1 C = ln 2 = ln x + ln 2 ln 1+y = ln x + C ln 1+y