Sr Examen
Ecuación diferencial xsqrt(x+y^2)dx+ysqrt(4+x^2)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
___________ ________
/ 2 / 2 d
x*\/ x + y (x) + \/ 4 + x *--(y(x))*y(x) = 0
dx
$$x \sqrt{x + y^{2}{\left(x \right)}} + \sqrt{x^{2} + 4} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x*sqrt(x + y^2) + sqrt(x^2 + 4)*y*y' = 0
Respuesta
[src]
/ _____ \
4 | / 2 1 | 5 / 3 3 3 \
x *|\/ C1 + --------| x *|- --- - ---------- + ----------|
_____ | 3/2| | 2 5/2 _____|
2 / 2 3 | / 2\ | | C1 / 2\ / 2 |
x *\/ C1 x \ \C1 / / \ 4*\C1 / 4*\/ C1 / / 6\
y(x) = C1 - ----------- - -------------- + ------------------------ + ------------------------------------ + O\x /
4*C1 _____ 64*C1 120*C1
/ 2
12*C1*\/ C1
$$y{\left(x \right)} = - \frac{x^{2} \sqrt{C_{1}^{2}}}{4 C_{1}} - \frac{x^{3}}{12 C_{1} \sqrt{C_{1}^{2}}} + \frac{x^{4} \left(\sqrt{C_{1}^{2}} + \frac{1}{\left(C_{1}^{2}\right)^{\frac{3}{2}}}\right)}{64 C_{1}} + \frac{x^{5} \left(\frac{3}{4 \sqrt{C_{1}^{2}}} - \frac{3}{4 \left(C_{1}^{2}\right)^{\frac{5}{2}}} - \frac{3}{C_{1}^{2}}\right)}{120 C_{1}} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, nan)
(-5.555555555555555, nan)
(-3.333333333333333, nan)
(-1.1111111111111107, nan)
(1.1111111111111107, nan)
(3.333333333333334, nan)
(5.555555555555557, nan)
(7.777777777777779, nan)
(10.0, nan)
(10.0, nan)