Solve differential equation L'(x)=k(x+b)(L-a)

Question
Solve differential equation \(L'(x)=k(x+b)(L-a)\)

Answers (1)

2020-12-18
\((dL)/(L-a)= k(x+b)dx\)
\((dL)/(L-a)= (kx+bk)dx\)
Now integrating both sides
\(int (dL)/(L-a)= int (kx+bk)dx\) \(ln(L-a)= (kx^2)/(2+bkx+c)\) (because \(int (1/(x+a)dx=ln(x+a))\) and \(int x^n dx= x^(n+1)/(n+1))\) where c is the constant of integration
So, the solution of the differential equation \(L'(x) = k(x+b)(L-a)\) will be \(ln(L-a)= (kx^2)/(2 + bkx + c)\)
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