Sr Examen
Ecuación diferencial dx*(e^y/x+1)-dy*(3*e^y+x)=0
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Solución
Ha introducido
[src]
y(x)
e d d y(x)
1 + ----- - x*--(y(x)) - 3*--(y(x))*e = 0
x dx dx
$$- x \frac{d}{d x} y{\left(x \right)} - 3 e^{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} + 1 + \frac{e^{y{\left(x \right)}}}{x} = 0$$
-x*y' - 3*exp(y)*y' + 1 + exp(y)/x = 0
Respuesta
[src]
/ __________\
|3 / 2 2*C1 |
2*C1 log(x) |\/ x *e |
y(x) = - ---- + ------ + W|-------------|
3 3 \ 3 /
$$y{\left(x \right)} = - \frac{2 C_{1}}{3} + \frac{\log{\left(x \right)}}{3} + W\left(\frac{\sqrt[3]{x^{2} e^{2 C_{1}}}}{3}\right)$$
/ __________ \
|3 / 2 2*C1 / ___\|
2*C1 log(x) |\/ x *e *\-1 + I*\/ 3 /|
y(x) = - ---- + ------ + W|----------------------------|
3 3 \ 6 /
$$y{\left(x \right)} = - \frac{2 C_{1}}{3} + \frac{\log{\left(x \right)}}{3} + W\left(\frac{\sqrt[3]{x^{2} e^{2 C_{1}}} \left(-1 + \sqrt{3} i\right)}{6}\right)$$
/ __________ \
| 3 / 2 2*C1 / ___\ |
2*C1 log(x) |-\/ x *e *\1 + I*\/ 3 / |
y(x) = - ---- + ------ + W|-----------------------------|
3 3 \ 6 /
$$y{\left(x \right)} = - \frac{2 C_{1}}{3} + \frac{\log{\left(x \right)}}{3} + W\left(- \frac{\sqrt[3]{x^{2} e^{2 C_{1}}} \left(1 + \sqrt{3} i\right)}{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
factorable
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.27860082790955465)
(-5.555555555555555, -0.25058138457354784)
(-3.333333333333333, -0.9686013474208157)
(-1.1111111111111107, -2.3700511890869596)
(1.1111111111111107, -40.70171190874166)
(3.333333333333334, 6.95205196045264e-310)
(5.555555555555557, 6.95205214039055e-310)
(7.777777777777779, 6.9520529151835e-310)
(10.0, 6.9520529151835e-310)
(10.0, 6.9520529151835e-310)