Sr Examen
Ecuación diferencial (6x+4y-18)dx+(4x+6y-22)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d d d
-18 - 22*--(y(x)) + 4*y(x) + 6*x + 4*x*--(y(x)) + 6*--(y(x))*y(x) = 0
dx dx dx
$$4 x \frac{d}{d x} y{\left(x \right)} + 6 x + 6 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 4 y{\left(x \right)} - 22 \frac{d}{d x} y{\left(x \right)} - 18 = 0$$
4*x*y' + 6*x + 6*y*y' + 4*y - 22*y' - 18 = 0
Respuesta
[src]
__________________
/ 2
11 2*x \/ C1 - 5*x + 10*x
y(x) = -- - --- - ---------------------
3 3 3
$$y{\left(x \right)} = - \frac{2 x}{3} - \frac{\sqrt{C_{1} - 5 x^{2} + 10 x}}{3} + \frac{11}{3}$$
__________________
/ 2
11 2*x \/ C1 - 5*x + 10*x
y(x) = -- - --- + ---------------------
3 3 3
$$y{\left(x \right)} = - \frac{2 x}{3} + \frac{\sqrt{C_{1} - 5 x^{2} + 10 x}}{3} + \frac{11}{3}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
linear coefficients
1st power series
lie group
1st exact Integral
linear coefficients Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -1.9304153854106885)
(-5.555555555555555, -4.25663820951169)
(-3.333333333333333, -6.302518003683786)
(-1.1111111111111107, -8.106045646236687)
(1.1111111111111107, -9.685800510982919)
(3.333333333333334, -11.04706511322987)
(5.555555555555557, -12.183353552706674)
(7.777777777777779, -13.074522427771281)
(10.0, -13.680003648647427)
(10.0, -13.680003648647427)