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xe^(x)+(x+1)e^(x)y=1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   x            x      
x*E  + (x + 1)*E *y = 1
exx+yex(x+1)=1e^{x} x + y e^{x} \left(x + 1\right) = 1
Simplificar
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
xex+y(x+1)ex=1x e^{x} + y \left(x + 1\right) e^{x} = 1
Коэффициент при y равен
(x+1)ex\left(x + 1\right) e^{x}
entonces son posibles los casos para x :
x<−1x < -1
x=−1x = -1
Consideremos todos los casos con detalles:
Con
x<−1x < -1
la ecuación será
−ye2−1−2e2=0- \frac{y}{e^{2}} - 1 - \frac{2}{e^{2}} = 0
su solución
y=−e2−2y = - e^{2} - 2
Con
x=−1x = -1
la ecuación será
−1−e−1=0-1 - e^{-1} = 0
su solución
no hay soluciones
Gráfica
Suma y producto de raíces [src] 
suma
  /                 /  -x \              /  -x \\                    /  -x \              /  -x \
  |/      /   x\\   | e   |     /   x\   | e   ||   /      /   x\\   | e   |     /   x\   | e   |
I*|\1 - re\x*e //*im|-----| - im\x*e /*re|-----|| + \1 - re\x*e //*re|-----| + im\x*e /*im|-----|
  \                 \1 + x/              \1 + x//                    \1 + x/              \1 + x/
(1−re⁡(xex))re⁡(e−xx+1)+i((1−re⁡(xex))im⁡(e−xx+1)−re⁡(e−xx+1)im⁡(xex))+im⁡(xex)im⁡(e−xx+1)\left(1 - \operatorname{re}{\left(x e^{x}\right)}\right) \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} + i \left(\left(1 - \operatorname{re}{\left(x e^{x}\right)}\right) \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} - \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} \operatorname{im}{\left(x e^{x}\right)}\right) + \operatorname{im}{\left(x e^{x}\right)} \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} 
=
  /                 /  -x \              /  -x \\                    /  -x \              /  -x \
  |/      /   x\\   | e   |     /   x\   | e   ||   /      /   x\\   | e   |     /   x\   | e   |
I*|\1 - re\x*e //*im|-----| - im\x*e /*re|-----|| + \1 - re\x*e //*re|-----| + im\x*e /*im|-----|
  \                 \1 + x/              \1 + x//                    \1 + x/              \1 + x/
(1−re⁡(xex))re⁡(e−xx+1)+i((1−re⁡(xex))im⁡(e−xx+1)−re⁡(e−xx+1)im⁡(xex))+im⁡(xex)im⁡(e−xx+1)\left(1 - \operatorname{re}{\left(x e^{x}\right)}\right) \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} + i \left(\left(1 - \operatorname{re}{\left(x e^{x}\right)}\right) \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} - \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} \operatorname{im}{\left(x e^{x}\right)}\right) + \operatorname{im}{\left(x e^{x}\right)} \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} 
producto
  /                 /  -x \              /  -x \\                    /  -x \              /  -x \
  |/      /   x\\   | e   |     /   x\   | e   ||   /      /   x\\   | e   |     /   x\   | e   |
I*|\1 - re\x*e //*im|-----| - im\x*e /*re|-----|| + \1 - re\x*e //*re|-----| + im\x*e /*im|-----|
  \                 \1 + x/              \1 + x//                    \1 + x/              \1 + x/
(1−re⁡(xex))re⁡(e−xx+1)+i((1−re⁡(xex))im⁡(e−xx+1)−re⁡(e−xx+1)im⁡(xex))+im⁡(xex)im⁡(e−xx+1)\left(1 - \operatorname{re}{\left(x e^{x}\right)}\right) \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} + i \left(\left(1 - \operatorname{re}{\left(x e^{x}\right)}\right) \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} - \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} \operatorname{im}{\left(x e^{x}\right)}\right) + \operatorname{im}{\left(x e^{x}\right)} \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} 
=
           /  -x \     /                  /  -x \              /  -x \\                     /  -x \
  /   x\   | e   |     |/       /   x\\   | e   |     /   x\   | e   ||   /       /   x\\   | e   |
im\x*e /*im|-----| - I*|\-1 + re\x*e //*im|-----| + im\x*e /*re|-----|| - \-1 + re\x*e //*re|-----|
           \1 + x/     \                  \1 + x/              \1 + x//                     \1 + x/
−i((re⁡(xex)−1)im⁡(e−xx+1)+re⁡(e−xx+1)im⁡(xex))−(re⁡(xex)−1)re⁡(e−xx+1)+im⁡(xex)im⁡(e−xx+1)- i \left(\left(\operatorname{re}{\left(x e^{x}\right)} - 1\right) \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} + \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} \operatorname{im}{\left(x e^{x}\right)}\right) - \left(\operatorname{re}{\left(x e^{x}\right)} - 1\right) \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} + \operatorname{im}{\left(x e^{x}\right)} \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} 
im(x*exp(x))*im(exp(-x)/(1 + x)) - i*((-1 + re(x*exp(x)))*im(exp(-x)/(1 + x)) + im(x*exp(x))*re(exp(-x)/(1 + x))) - (-1 + re(x*exp(x)))*re(exp(-x)/(1 + x))
Respuesta rápida [src] 
       /                 /  -x \              /  -x \\                    /  -x \              /  -x \
       |/      /   x\\   | e   |     /   x\   | e   ||   /      /   x\\   | e   |     /   x\   | e   |
y1 = I*|\1 - re\x*e //*im|-----| - im\x*e /*re|-----|| + \1 - re\x*e //*re|-----| + im\x*e /*im|-----|
       \                 \1 + x/              \1 + x//                    \1 + x/              \1 + x/
y1=(1−re⁡(xex))re⁡(e−xx+1)+i((1−re⁡(xex))im⁡(e−xx+1)−re⁡(e−xx+1)im⁡(xex))+im⁡(xex)im⁡(e−xx+1)y_{1} = \left(1 - \operatorname{re}{\left(x e^{x}\right)}\right) \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} + i \left(\left(1 - \operatorname{re}{\left(x e^{x}\right)}\right) \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} - \operatorname{re}{\left(\frac{e^{- x}}{x + 1}\right)} \operatorname{im}{\left(x e^{x}\right)}\right) + \operatorname{im}{\left(x e^{x}\right)} \operatorname{im}{\left(\frac{e^{- x}}{x + 1}\right)} 
y1 = (1 - re(x*exp(x)))*re(exp(-x)/(x + 1)) + i*((1 - re(x*exp(x)))*im(exp(-x)/(x + 1)) - re(exp(-x)/(x + 1))*im(x*exp(x))) + im(x*exp(x))*im(exp(-x)/(x + 1))
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