Question

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

First order differential equations
ANSWERED
asked 2020-12-17
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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