Sr Examen
Ecuación diferencial exp(x)*cos(y)^2*dx+(1-exp(x))dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 x d x d
cos (y(x))*e - --(y(x))*e + --(y(x)) = 0
dx dx
$$e^{x} \cos^{2}{\left(y{\left(x \right)} \right)} - e^{x} \frac{d}{d x} y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$
exp(x)*cos(y)^2 - exp(x)*y' + y' = 0
Respuesta
[src]
/ _____________________________________________\
| / 2 2/ x\ / x\ |
|-1 + \/ 1 + C1 + log \-1 + e / + 2*C1*log\-1 + e / |
y(x) = 2*atan|-----------------------------------------------------|
| / x\ |
\ C1 + log\-1 + e / /
$$y{\left(x \right)} = 2 \operatorname{atan}{\left(\frac{\sqrt{C_{1}^{2} + 2 C_{1} \log{\left(e^{x} - 1 \right)} + \log{\left(e^{x} - 1 \right)}^{2} + 1} - 1}{C_{1} + \log{\left(e^{x} - 1 \right)}} \right)}$$
/ _____________________________________________\
| / 2 2/ x\ / x\ |
|1 + \/ 1 + C1 + log \-1 + e / + 2*C1*log\-1 + e / |
y(x) = -2*atan|----------------------------------------------------|
| / x\ |
\ C1 + log\-1 + e / /
$$y{\left(x \right)} = - 2 \operatorname{atan}{\left(\frac{\sqrt{C_{1}^{2} + 2 C_{1} \log{\left(e^{x} - 1 \right)} + \log{\left(e^{x} - 1 \right)}^{2} + 1} + 1}{C_{1} + \log{\left(e^{x} - 1 \right)}} \right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.7497998529051708)
(-5.555555555555555, 0.7479464458006942)
(-3.333333333333333, 0.730220705697849)
(-1.1111111111111107, 0.48920412716882483)
(1.1111111111111107, -1.5412146222008565)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 3.1237768967464496e-33)
(7.777777777777779, 8.388243571827863e+296)
(10.0, 3.4850068345956685e-196)
(10.0, 3.4850068345956685e-196)