(a)
\The differential equation is .
The differential equation passes through the point .
Seperate the variables by bringing terms to the left side of the equation.
Integrate on both sides.
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From logarithm and power rule.
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From the logarithm exponential rule.
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.
This equation passes throught the point .
Substitute the value in .
Sketch two approximate solutions of the differential equation on the slope field.
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(b)
\The particular solution of the differential equation is .
Graph :
\(1) Draw the coordinate plane.
\(2) Graph the function .
(a)
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(b)
\The particular solutions of the differential equation is .