# Solving differential equation gives complex number

Posted 4 months ago
609 Views
|
2 Replies
|
1 Total Likes
|
 Differential Equation Modeling a DiseaseI have been trying to sole the following IVP but get an answer with complex solutions although ALL the parameters are real. eq = i'[t] + (\[Gamma] + \[Mu] - \[Lambda]) i[t] == -\[Lambda] i[t]^2 DSolve[{eq, i[0] == i0}, i[t], t] How should I use the fact that all parameters are real as is i and t ? Thank you Attachments:
2 Replies
Sort By:
Posted 4 months ago
 The solution uses complex numbers, but its values are real and correct: sol1 = DSolveValue[{eq, i[0] == i0}, i, t] FullSimplify[{eq, i[0] == i0} /. i -> sol1] Block[{\[Gamma] = 1, \[Mu] = 1, \[Lambda] = 1, i0 = 1}, Plot[sol1[t], {t, 0, 1}]] You can get an expression that uses only real objects this way: sol = DSolveValue[eq, i, t] param = Solve[sol[0] == i0, C[1], Reals] mySol[t_] = FullSimplify[ sol[t] /. param[[1]] /. ConditionalExpression -> (#1 &)] Simplify[{eq, i[0] == i0} /. i -> mySol]