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e/p=-(u/p)-l*p*i-(1/(c*p))*(u/(p*r)+o/(c*p*r)) equation

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Numerical solution:

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The solution

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                   u      o  
                  --- + -----
E     u           p*r   c*p*r
- = - - - l*p*I - -----------
p     p               c*p
$$\frac{e}{p} = \left(- i l p - \frac{u}{p}\right) - \frac{\frac{o}{r c p} + \frac{u}{p r}}{c p}$$
Simplify
The graph
Rapid solution [src] 
       /  /    /     2  3\       /     2\        \   /      1      \   /    /     2\             /     2  3\\   /      1      \\   /    /     2\             /     2  3\\   /      1      \   /    /     2  3\       /     2\        \   /      1      \
u1 = I*|- \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*im|-------------| - \E*im\p*r*c / + im(o) + re\l*r*c *p //*re|-------------|| + \E*im\p*r*c / + im(o) + re\l*r*c *p //*im|-------------| - \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*re|-------------|
       \                                             \c*(1 + c*p*r)/                                            \c*(1 + c*p*r)//                                            \c*(1 + c*p*r)/                                              \c*(1 + c*p*r)/
$$u_{1} = i \left(- \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} - \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}\right) - \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} + \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}$$ 
u1 = i*(-(re(o) + E*re(c^2*p*r) - im(c^2*l*p^3*r))*im(1/(c*(c*p*r + 1))) - (re(c^2*l*p^3*r) + im(o) + E*im(c^2*p*r))*re(1/(c*(c*p*r + 1)))) - (re(o) + E*re(c^2*p*r) - im(c^2*l*p^3*r))*re(1/(c*(c*p*r + 1))) + (re(c^2*l*p^3*r) + im(o) + E*im(c^2*p*r))*im(1/(c*(c*p*r + 1)))
Sum and product of roots [src] 
sum
  /  /    /     2  3\       /     2\        \   /      1      \   /    /     2\             /     2  3\\   /      1      \\   /    /     2\             /     2  3\\   /      1      \   /    /     2  3\       /     2\        \   /      1      \
I*|- \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*im|-------------| - \E*im\p*r*c / + im(o) + re\l*r*c *p //*re|-------------|| + \E*im\p*r*c / + im(o) + re\l*r*c *p //*im|-------------| - \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*re|-------------|
  \                                             \c*(1 + c*p*r)/                                            \c*(1 + c*p*r)//                                            \c*(1 + c*p*r)/                                              \c*(1 + c*p*r)/
$$i \left(- \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} - \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}\right) - \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} + \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}$$ 
=
  /  /    /     2  3\       /     2\        \   /      1      \   /    /     2\             /     2  3\\   /      1      \\   /    /     2\             /     2  3\\   /      1      \   /    /     2  3\       /     2\        \   /      1      \
I*|- \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*im|-------------| - \E*im\p*r*c / + im(o) + re\l*r*c *p //*re|-------------|| + \E*im\p*r*c / + im(o) + re\l*r*c *p //*im|-------------| - \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*re|-------------|
  \                                             \c*(1 + c*p*r)/                                            \c*(1 + c*p*r)//                                            \c*(1 + c*p*r)/                                              \c*(1 + c*p*r)/
$$i \left(- \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} - \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}\right) - \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} + \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}$$ 
product
  /  /    /     2  3\       /     2\        \   /      1      \   /    /     2\             /     2  3\\   /      1      \\   /    /     2\             /     2  3\\   /      1      \   /    /     2  3\       /     2\        \   /      1      \
I*|- \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*im|-------------| - \E*im\p*r*c / + im(o) + re\l*r*c *p //*re|-------------|| + \E*im\p*r*c / + im(o) + re\l*r*c *p //*im|-------------| - \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*re|-------------|
  \                                             \c*(1 + c*p*r)/                                            \c*(1 + c*p*r)//                                            \c*(1 + c*p*r)/                                              \c*(1 + c*p*r)/
$$i \left(- \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} - \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}\right) - \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} + \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}$$ 
=
/    /     2\             /     2  3\\   /      1      \     //    /     2  3\       /     2\        \   /      1      \   /    /     2\             /     2  3\\   /      1      \\   /    /     2  3\       /     2\        \   /      1      \
\E*im\p*r*c / + im(o) + re\l*r*c *p //*im|-------------| - I*|\- im\l*r*c *p / + E*re\p*r*c / + re(o)/*im|-------------| + \E*im\p*r*c / + im(o) + re\l*r*c *p //*re|-------------|| - \- im\l*r*c *p / + E*re\p*r*c / + re(o)/*re|-------------|
                                         \c*(1 + c*p*r)/     \                                           \c*(1 + c*p*r)/                                            \c*(1 + c*p*r)//                                              \c*(1 + c*p*r)/
$$- i \left(\left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} + \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}\right) - \left(\operatorname{re}{\left(o\right)} + e \operatorname{re}{\left(c^{2} p r\right)} - \operatorname{im}{\left(c^{2} l p^{3} r\right)}\right) \operatorname{re}{\left(\frac{1}{c \left(c p r + 1\right)}\right)} + \left(\operatorname{re}{\left(c^{2} l p^{3} r\right)} + \operatorname{im}{\left(o\right)} + e \operatorname{im}{\left(c^{2} p r\right)}\right) \operatorname{im}{\left(\frac{1}{c \left(c p r + 1\right)}\right)}$$ 
(E*im(p*r*c^2) + im(o) + re(l*r*c^2*p^3))*im(1/(c*(1 + c*p*r))) - i*((-im(l*r*c^2*p^3) + E*re(p*r*c^2) + re(o))*im(1/(c*(1 + c*p*r))) + (E*im(p*r*c^2) + im(o) + re(l*r*c^2*p^3))*re(1/(c*(1 + c*p*r)))) - (-im(l*r*c^2*p^3) + E*re(p*r*c^2) + re(o))*re(1/(c*(1 + c*p*r)))
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