SOLUTION: Solve by integration {{{dx/dt = t(x

SOLUTION: Solve by integration {{{dx/dt = t(x - 2)}}}

Question 1145007: Solve by integration
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!



Multiply both sides by dt:



The term on the right side contains two variables, t and x. We must get rid
of the other variable besides the variable of the differential.  The variable
of the differential on the right side is t (because we have dt), so we must
get rid of the (x - 2) factor.  So we divide both sides by (x - 2):







We integrate both sides:



We use the formula  on the left side,
and we use the formula  on the right side:






Since the left side is positive, we can dispense with the absolute value on the
right side and require that x>2.





Since e^C₁ is an arbitrary constant, we can let it be C.





Edwin

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