Sr Examen
Ecuación diferencial dy\dx=-4x+3y\2x+y
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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d 3*x*y(x) --(y(x)) = -4*x + -------- + y(x) dx 2
$$\frac{d}{d x} y{\left(x \right)} = \frac{3 x y{\left(x \right)}}{2} - 4 x + y{\left(x \right)}$$
y' = 3*x*y/2 - 4*x + y
Respuesta
[src]
2
1 3*x
/ ___ \ - + x + ----
/ 3*x\ ___ ____ |\/ 3 *(2 + 3*x)| 3 4
x*|1 + ---| 8*\/ 3 *\/ pi *erf|---------------|*e
8 \ 4 / \ 6 /
y(x) = - + C1*e + -------------------------------------------------
3 9
$$y{\left(x \right)} = C_{1} e^{x \left(\frac{3 x}{4} + 1\right)} + \frac{8 \sqrt{3} \sqrt{\pi} e^{\frac{3 x^{2}}{4} + x + \frac{1}{3}} \operatorname{erf}{\left(\frac{\sqrt{3} \left(3 x + 2\right)}{6} \right)}}{9} + \frac{8}{3}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st linear
almost linear
1st power series
lie group
1st exact Integral
1st linear Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 2.9134932260468283)
(-5.555555555555555, 3.020909262544519)
(-3.333333333333333, 3.2832324548033442)
(-1.1111111111111107, 4.52181653757663)
(1.1111111111111107, 60.211734028753206)
(3.333333333333334, 888276.5366089876)
(5.555555555555557, 22265799418204.04)
(7.777777777777779, 9.198682937010517e+23)
(10.0, 6.263385915066702e+37)
(10.0, 6.263385915066702e+37)